Question

A) A group of Mathematics faculty at the local college consists of 9 women and 10 men. Four people are to be selected to go to a conference.
a. How many different ways can a group of four people be selected from this group of 19?
   

b. In how many ways can four women be chosen from the group of 9 women?
   

c. What is the probability that all women will be chosen to attend the conference?
Enter a reduced fraction or decimal.

B) Jacob buys a bag of cookies that contains 7 chocolate chip cookies, 5 peanut butter cookies, 8 sugar cookies and 5 oatmeal cookies.

What is the probability that Jacob reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie?

Answer 1

solution:

A)4 people from 19 can be selected by 19C4=19*18*17*16/4*3*2*1=3876

B) FOUR women selected from 9 is =9C4=126 ways

c)the probability that all women will be chosen to attend conference=126/3876=0.0325

b)Given that , chocolate chip cookies = 7, peanut butter cookies = 5 , sugar cookies = 8 , oatmeal cookies = 5

total=7+5+8+5=25

Probability of selecting a peanut butter cookies = 5/25

Probability of selecting a sugar cookies = 8/24

p(peanut butter and sugar cookies)=5/25*8/24

= 40/600

=0.06667