Question

Answer the questions below. (a) How many different committees of size 3 can be formed from 14 people? (b) There are 12 European cities that Alice would eventually like to visit. On her next vacation, though, she only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. She is now trying to make a schedule of which city she'll visit on which day. How many different schedules are possible? (Assume that she will not visit a city more than once.)

Answer 1

a.

Number of people ( n) = 14

A committee of 3 people is to be formed.

Therefore the number of ways such committee can be formed

=

14 3

= $\frac{14!}{3! (14-3)!}$

= 364

Therefore the number of different committees of size 3 is 364.

b.

Alice has 3 days to visit 3 places.

Therefore the number of different possible schedule = n!

= 3! = 6

Therefore the numnumber of different schedule is 6.