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Problem:

The Coupland family has six children and four adults. They want to get some corn dogs, but their van can only hold four children and two adults. How many ways can the people in the van be chosen?

rohitaop  May 28, 2018
#1
+7002
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The problem can be divided into:

(1) How to choose 4 children from 6 children;

(2) How to choose 2 adults from 4 adults.

Number of ways

$$= \displaystyle\binom6 4\cdot \binom4 2$$

$$=\dfrac{6!}{4!(6-4)!}\cdot\dfrac{4!}{2!(4-2)!}\\ =\dfrac{6!}{(2!)^3}\\ =90$$

MaxWong  May 28, 2018