Question

5. Which scenario or scenarios below are represented by 9????3?

a. The number of ways 3 of 9 people can sit in a row of 3 chairs
b. The number of ways to pick 3 students out of 9 students to attend an art workshop
c. The number of ways to pick 3 different entrees from a buffet line of 9 different entrees

Answer 1

b. and c. are correct.

Explanation:

The combinatorial number
`{9 \choose 3}` represents the total amount of ways to pick 3 different elements from a set of 9, ignoring order.

In the first case we do care about order because it is not the same for a person to sit on the first chiar or the second one.

Even tough (c) does not specify anything, when you pick an entry, you may care about order because either you want to eat them in a specific order or because you are ordering entrees for 3 different people. however, since the exrecise doesnt say anything, it is better to assume that order doesnt matter, so there are a total of
`{9 \choose 3}` possibilities to choose.

In (b) order doesnt matter, and you are picking 3 studdents out of a group of 9, so there are
`{9 \choose 3}` possibilities.