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rodikova [14]
3 years ago
7

Suppose that a teacher wishes to distribute 25 identical pencils to Ahmed, Barbara, Casper, and Dieter such that Ahmed and Diete

r receive at least one pencil each, Casper receives no more than five pencils, and Barbara receives at least four pencils. In how many ways can such a distribution be made?
Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
5 0

Answer:

we will change the problem in stages

pre-place 1 in x1 & x4, and 4 in x2, thus guaranteeing their minimum requirements.

now 19 pencils remain to be distributed

when there are no restrictions on distributing n identical objects to k distinct piles, the formula is (n+k-1)C(k-1) which here translates to 22C3

finally, we need to see that x3 = 5, so we place 6 in x3 (guaranteeing that it violates the condition), and subtract such violations, ie (22-6)C3 = 16C3

ans: 22C3 - 16C3 = 980

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