Question

from a group of 6 men and 7 women going on a trip, find the number of
a) ways of selecting a female tour guide, a female cook and a driver of either sex
b) ways of selecting a commitee of 5 people with 4 or more men

Answer 1

7 ways for tour guide, then 6 ways for cook then 11 ways for driver
7 * 6 * 11

combinations of 5 out of the six men at a time
6!/[ 5!(1!)] = 6
combinations of 4 out of the 6 men
6!/[ 4!(2!)] = 6*5/2 = 15
If we have 4 men, then one of the 7 women must serve (we have already included the remaining two men in the five men option)
so for each combination of 4 men we have a choice of 7 women
so in all
6 + 15 * 7

Answer 2

since there is a title for a job so

(7 choose 2)(11 choose 1)

11 because u already choose 2 women