Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y leq 7$

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Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y leq 7$. This problem is found in the book How to Count by Beeler which contains no solutions, so I have no way of verifying the correct solution.







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  • show us your try
    – pointguard0
    Aug 22 at 6:32














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Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y leq 7$. This problem is found in the book How to Count by Beeler which contains no solutions, so I have no way of verifying the correct solution.







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  • show us your try
    – pointguard0
    Aug 22 at 6:32












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y leq 7$. This problem is found in the book How to Count by Beeler which contains no solutions, so I have no way of verifying the correct solution.







share|cite|improve this question














Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y leq 7$. This problem is found in the book How to Count by Beeler which contains no solutions, so I have no way of verifying the correct solution.









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edited Aug 22 at 6:41

























asked Aug 22 at 6:22









Frank Aiello

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  • show us your try
    – pointguard0
    Aug 22 at 6:32
















  • show us your try
    – pointguard0
    Aug 22 at 6:32















show us your try
– pointguard0
Aug 22 at 6:32




show us your try
– pointguard0
Aug 22 at 6:32










1 Answer
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Hint: Add the number of integer solutions of the equation $2x+3y=n$ for $n=1,2,ldots,7.$






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  • We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well.
    – N. F. Taussig
    Aug 22 at 7:20










  • yes, if $0$ is an integer
    – Leox
    Aug 22 at 7:25










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
3
down vote



accepted










Hint: Add the number of integer solutions of the equation $2x+3y=n$ for $n=1,2,ldots,7.$






share|cite|improve this answer




















  • We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well.
    – N. F. Taussig
    Aug 22 at 7:20










  • yes, if $0$ is an integer
    – Leox
    Aug 22 at 7:25














up vote
3
down vote



accepted










Hint: Add the number of integer solutions of the equation $2x+3y=n$ for $n=1,2,ldots,7.$






share|cite|improve this answer




















  • We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well.
    – N. F. Taussig
    Aug 22 at 7:20










  • yes, if $0$ is an integer
    – Leox
    Aug 22 at 7:25












up vote
3
down vote



accepted







up vote
3
down vote



accepted






Hint: Add the number of integer solutions of the equation $2x+3y=n$ for $n=1,2,ldots,7.$






share|cite|improve this answer












Hint: Add the number of integer solutions of the equation $2x+3y=n$ for $n=1,2,ldots,7.$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 22 at 6:54









Leox

5,1141323




5,1141323











  • We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well.
    – N. F. Taussig
    Aug 22 at 7:20










  • yes, if $0$ is an integer
    – Leox
    Aug 22 at 7:25
















  • We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well.
    – N. F. Taussig
    Aug 22 at 7:20










  • yes, if $0$ is an integer
    – Leox
    Aug 22 at 7:25















We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well.
– N. F. Taussig
Aug 22 at 7:20




We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well.
– N. F. Taussig
Aug 22 at 7:20












yes, if $0$ is an integer
– Leox
Aug 22 at 7:25




yes, if $0$ is an integer
– Leox
Aug 22 at 7:25












 

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