transformation of an equation (Binomial coefficient) [closed]
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Good afternoon
I don't understand this transformation. Can you please help me?
Greetings
Ava
$beginalignn choose k&=fracn1cdotfracn-12cdotsfracn-(k-1)k\&=fracncdot (n-1)cdots(n-k+1)k!endalign$
binomial-coefficients transformation
closed as off-topic by amWhy, Jyrki Lahtonen, José Carlos Santos, Theoretical Economist, Adrian Keister Sep 9 at 0:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." â amWhy, Theoretical Economist, Adrian Keister
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up vote
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Good afternoon
I don't understand this transformation. Can you please help me?
Greetings
Ava
$beginalignn choose k&=fracn1cdotfracn-12cdotsfracn-(k-1)k\&=fracncdot (n-1)cdots(n-k+1)k!endalign$
binomial-coefficients transformation
closed as off-topic by amWhy, Jyrki Lahtonen, José Carlos Santos, Theoretical Economist, Adrian Keister Sep 9 at 0:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." â amWhy, Theoretical Economist, Adrian Keister
the above part is just a multiplication $n-(k-1)=n-1cdot(k-1)=n-k+1$... The below part is just the definition of $k!$
â koleygr
Sep 8 at 12:19
Welcome to MathSE. Please read this tutorial, which explains how to typeset mathematics on this site using MathJax.
â N. F. Taussig
Sep 8 at 13:29
@N.F.Taussig Is it possible to remove the central = between lines by Latex?
â Narasimham
Sep 8 at 23:03
@Narasimham Somebody left an extra equals sign after the aligned equations, producing the central equals sign you noticed.
â N. F. Taussig
Sep 8 at 23:16
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Good afternoon
I don't understand this transformation. Can you please help me?
Greetings
Ava
$beginalignn choose k&=fracn1cdotfracn-12cdotsfracn-(k-1)k\&=fracncdot (n-1)cdots(n-k+1)k!endalign$
binomial-coefficients transformation
Good afternoon
I don't understand this transformation. Can you please help me?
Greetings
Ava
$beginalignn choose k&=fracn1cdotfracn-12cdotsfracn-(k-1)k\&=fracncdot (n-1)cdots(n-k+1)k!endalign$
binomial-coefficients transformation
binomial-coefficients transformation
edited Sep 8 at 23:15
N. F. Taussig
39.7k93153
39.7k93153
asked Sep 8 at 11:46
user591158
closed as off-topic by amWhy, Jyrki Lahtonen, José Carlos Santos, Theoretical Economist, Adrian Keister Sep 9 at 0:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." â amWhy, Theoretical Economist, Adrian Keister
closed as off-topic by amWhy, Jyrki Lahtonen, José Carlos Santos, Theoretical Economist, Adrian Keister Sep 9 at 0:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." â amWhy, Theoretical Economist, Adrian Keister
the above part is just a multiplication $n-(k-1)=n-1cdot(k-1)=n-k+1$... The below part is just the definition of $k!$
â koleygr
Sep 8 at 12:19
Welcome to MathSE. Please read this tutorial, which explains how to typeset mathematics on this site using MathJax.
â N. F. Taussig
Sep 8 at 13:29
@N.F.Taussig Is it possible to remove the central = between lines by Latex?
â Narasimham
Sep 8 at 23:03
@Narasimham Somebody left an extra equals sign after the aligned equations, producing the central equals sign you noticed.
â N. F. Taussig
Sep 8 at 23:16
add a comment |Â
the above part is just a multiplication $n-(k-1)=n-1cdot(k-1)=n-k+1$... The below part is just the definition of $k!$
â koleygr
Sep 8 at 12:19
Welcome to MathSE. Please read this tutorial, which explains how to typeset mathematics on this site using MathJax.
â N. F. Taussig
Sep 8 at 13:29
@N.F.Taussig Is it possible to remove the central = between lines by Latex?
â Narasimham
Sep 8 at 23:03
@Narasimham Somebody left an extra equals sign after the aligned equations, producing the central equals sign you noticed.
â N. F. Taussig
Sep 8 at 23:16
the above part is just a multiplication $n-(k-1)=n-1cdot(k-1)=n-k+1$... The below part is just the definition of $k!$
â koleygr
Sep 8 at 12:19
the above part is just a multiplication $n-(k-1)=n-1cdot(k-1)=n-k+1$... The below part is just the definition of $k!$
â koleygr
Sep 8 at 12:19
Welcome to MathSE. Please read this tutorial, which explains how to typeset mathematics on this site using MathJax.
â N. F. Taussig
Sep 8 at 13:29
Welcome to MathSE. Please read this tutorial, which explains how to typeset mathematics on this site using MathJax.
â N. F. Taussig
Sep 8 at 13:29
@N.F.Taussig Is it possible to remove the central = between lines by Latex?
â Narasimham
Sep 8 at 23:03
@N.F.Taussig Is it possible to remove the central = between lines by Latex?
â Narasimham
Sep 8 at 23:03
@Narasimham Somebody left an extra equals sign after the aligned equations, producing the central equals sign you noticed.
â N. F. Taussig
Sep 8 at 23:16
@Narasimham Somebody left an extra equals sign after the aligned equations, producing the central equals sign you noticed.
â N. F. Taussig
Sep 8 at 23:16
add a comment |Â
1 Answer
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By definition $$binomnk=fracn!k!(n-k)!=fracn(n-1)ldots(n-k+1)(n-k)!k!(n-k)!$$
Cancel out the$ (n-k)!$ and you're done.
Good evening But I don't understand how to get from n factorial to this equation in the numerator. greetings ava
â user591158
Sep 8 at 16:34
Good evening @Ava .. Well imagine $k=3$ and $n=5$.. couldn't you write $5!$ as $5.4.3.2!$ where $2!=(n-k)!$?
â Ahmad Bazzi
Sep 8 at 17:42
But n factorial should be n(n-1)(n-2).... But why n(n-1)(n-2)...(n-k+1)(n-k)factorial
â user591158
Sep 8 at 18:05
Mathematically $n(n-1)(n-2)....(2)(1) = n(n-1)(n-2)...(n-k+1)(n-k)!$
â Ahmad Bazzi
Sep 8 at 19:42
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
By definition $$binomnk=fracn!k!(n-k)!=fracn(n-1)ldots(n-k+1)(n-k)!k!(n-k)!$$
Cancel out the$ (n-k)!$ and you're done.
Good evening But I don't understand how to get from n factorial to this equation in the numerator. greetings ava
â user591158
Sep 8 at 16:34
Good evening @Ava .. Well imagine $k=3$ and $n=5$.. couldn't you write $5!$ as $5.4.3.2!$ where $2!=(n-k)!$?
â Ahmad Bazzi
Sep 8 at 17:42
But n factorial should be n(n-1)(n-2).... But why n(n-1)(n-2)...(n-k+1)(n-k)factorial
â user591158
Sep 8 at 18:05
Mathematically $n(n-1)(n-2)....(2)(1) = n(n-1)(n-2)...(n-k+1)(n-k)!$
â Ahmad Bazzi
Sep 8 at 19:42
add a comment |Â
up vote
1
down vote
By definition $$binomnk=fracn!k!(n-k)!=fracn(n-1)ldots(n-k+1)(n-k)!k!(n-k)!$$
Cancel out the$ (n-k)!$ and you're done.
Good evening But I don't understand how to get from n factorial to this equation in the numerator. greetings ava
â user591158
Sep 8 at 16:34
Good evening @Ava .. Well imagine $k=3$ and $n=5$.. couldn't you write $5!$ as $5.4.3.2!$ where $2!=(n-k)!$?
â Ahmad Bazzi
Sep 8 at 17:42
But n factorial should be n(n-1)(n-2).... But why n(n-1)(n-2)...(n-k+1)(n-k)factorial
â user591158
Sep 8 at 18:05
Mathematically $n(n-1)(n-2)....(2)(1) = n(n-1)(n-2)...(n-k+1)(n-k)!$
â Ahmad Bazzi
Sep 8 at 19:42
add a comment |Â
up vote
1
down vote
up vote
1
down vote
By definition $$binomnk=fracn!k!(n-k)!=fracn(n-1)ldots(n-k+1)(n-k)!k!(n-k)!$$
Cancel out the$ (n-k)!$ and you're done.
By definition $$binomnk=fracn!k!(n-k)!=fracn(n-1)ldots(n-k+1)(n-k)!k!(n-k)!$$
Cancel out the$ (n-k)!$ and you're done.
answered Sep 8 at 13:23
Ahmad Bazzi
6,4061624
6,4061624
Good evening But I don't understand how to get from n factorial to this equation in the numerator. greetings ava
â user591158
Sep 8 at 16:34
Good evening @Ava .. Well imagine $k=3$ and $n=5$.. couldn't you write $5!$ as $5.4.3.2!$ where $2!=(n-k)!$?
â Ahmad Bazzi
Sep 8 at 17:42
But n factorial should be n(n-1)(n-2).... But why n(n-1)(n-2)...(n-k+1)(n-k)factorial
â user591158
Sep 8 at 18:05
Mathematically $n(n-1)(n-2)....(2)(1) = n(n-1)(n-2)...(n-k+1)(n-k)!$
â Ahmad Bazzi
Sep 8 at 19:42
add a comment |Â
Good evening But I don't understand how to get from n factorial to this equation in the numerator. greetings ava
â user591158
Sep 8 at 16:34
Good evening @Ava .. Well imagine $k=3$ and $n=5$.. couldn't you write $5!$ as $5.4.3.2!$ where $2!=(n-k)!$?
â Ahmad Bazzi
Sep 8 at 17:42
But n factorial should be n(n-1)(n-2).... But why n(n-1)(n-2)...(n-k+1)(n-k)factorial
â user591158
Sep 8 at 18:05
Mathematically $n(n-1)(n-2)....(2)(1) = n(n-1)(n-2)...(n-k+1)(n-k)!$
â Ahmad Bazzi
Sep 8 at 19:42
Good evening But I don't understand how to get from n factorial to this equation in the numerator. greetings ava
â user591158
Sep 8 at 16:34
Good evening But I don't understand how to get from n factorial to this equation in the numerator. greetings ava
â user591158
Sep 8 at 16:34
Good evening @Ava .. Well imagine $k=3$ and $n=5$.. couldn't you write $5!$ as $5.4.3.2!$ where $2!=(n-k)!$?
â Ahmad Bazzi
Sep 8 at 17:42
Good evening @Ava .. Well imagine $k=3$ and $n=5$.. couldn't you write $5!$ as $5.4.3.2!$ where $2!=(n-k)!$?
â Ahmad Bazzi
Sep 8 at 17:42
But n factorial should be n(n-1)(n-2).... But why n(n-1)(n-2)...(n-k+1)(n-k)factorial
â user591158
Sep 8 at 18:05
But n factorial should be n(n-1)(n-2).... But why n(n-1)(n-2)...(n-k+1)(n-k)factorial
â user591158
Sep 8 at 18:05
Mathematically $n(n-1)(n-2)....(2)(1) = n(n-1)(n-2)...(n-k+1)(n-k)!$
â Ahmad Bazzi
Sep 8 at 19:42
Mathematically $n(n-1)(n-2)....(2)(1) = n(n-1)(n-2)...(n-k+1)(n-k)!$
â Ahmad Bazzi
Sep 8 at 19:42
add a comment |Â
the above part is just a multiplication $n-(k-1)=n-1cdot(k-1)=n-k+1$... The below part is just the definition of $k!$
â koleygr
Sep 8 at 12:19
Welcome to MathSE. Please read this tutorial, which explains how to typeset mathematics on this site using MathJax.
â N. F. Taussig
Sep 8 at 13:29
@N.F.Taussig Is it possible to remove the central = between lines by Latex?
â Narasimham
Sep 8 at 23:03
@Narasimham Somebody left an extra equals sign after the aligned equations, producing the central equals sign you noticed.
â N. F. Taussig
Sep 8 at 23:16