Question

(Probability with Permutations and Combinations) I’m not sure how to solve this problem/how to get the answer, need help!

Answer 1

The "explanation" for the problem has a typo in it. There are 11 possible ice cream/yogurt flavors to choose from, regardless of whether any are low-fat, so the total number of ways of choosing any 2 from the selection is

$11\mathrm C2=\dfrac{11!}{2!(11-2)!}=55$


In particular we want to count the number of ways of picking 1 ice cream and 1 yogurt flavor from the low-fat variety. There are 6 total choices that are not low-fat of which we choose 0, 3 choices of low-fat ice cream of which we choose 1, and 2 choices of low-fat yogurt of which we also choose 1. In terms of the binomial coefficient, this is

$(6\mathrm C0)\cdot(3\mathrm C1)\cdot(2\mathrm C1)=1\cdot3\cdot2=6$

So the probability of getting such a combination is $\dfrac6{55}$.