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Students have given \(15\) coffee packets to \(3\) teachers. Suppose that Eric demands he receives an even number of coffee packets and Alan demands he receives an odd amount. How many ways are there to distribute the packets?

 Nov 27, 2022
 #1
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There are 45 ways to distribute the packets.

 Nov 27, 2022
 #2
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Without a minimum number of packets to each teacher, then you have:

 

(12, 2, 1) , (10, 4, 1) , (8, 6, 1) , (6, 8, 1) , (4, 10, 1) , (2, 12, 1) , (10, 2, 3) , (8, 4, 3) , (6, 6, 3) , (4, 8, 3) , (2, 10, 3) , (8, 2, 5) , (6, 4, 5) , (4, 6, 5) , (2, 8, 5) , (6, 2, 7) , (4, 4, 7) , (2, 6, 7) , (4, 2, 9) , (2, 4, 9) , (2, 2, 11) , (12, 1, 2) , (10, 3, 2) , (8, 5, 2) , (6, 7, 2) , (4, 9, 2) , (2, 11, 2) , (10, 1, 4) , (8, 3, 4) , (6, 5, 4) , (4, 7, 4) , (2, 9, 4) , (8, 1, 6) , (6, 3, 6) , (4, 5, 6) , (2, 7, 6) , (6, 1, 8) , (4, 3, 8) , (2, 5, 8) , (4, 1, 10) , (2, 3, 10) , (2, 1, 12) , (11, 2, 2) , (9, 4, 2) , (7, 6, 2) , (5, 8, 2) , (3, 10, 2) , (1, 12, 2) , (9, 2, 4) , (7, 4, 4) , (5, 6, 4) , (3, 8, 4) , (1, 10, 4) , (7, 2, 6) , (5, 4, 6) , (3, 6, 6) , (1, 8, 6) , (5, 2, 8) , (3, 4, 8) , (1, 6, 8) , (3, 2, 10) , (1, 4, 10) , (1, 2, 12)==63 different ways

 

 

Note: The sum of each permutation ==15 and each permutation consists of: Two EVEN numbers + one ODD number.

 Nov 27, 2022

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