Probability

[mathwhizwannabe]

A committee of 5 is to be chosen from 4 men and 3 women.

a. How many different 5-person committees are possible?

b. Find the probability that the committee includes:

(1) 2 men and 3 women
(2) 3 men and 2 women
(3) at least 2 women
(4) all women

c. In how many ways can this 5-person committee select a chairperson and a secretary?

d. If Hilda and Joan are on the committee, what is the probability that one is selected as chairperson, and the other as secretary?


My answers:
a. 21
b. (1) 2/7
(2) 4/7
(3) 6/7
(4) 0
c. 20
d. 1/10

I think a and b are correct, but I am not sure about c and d. Can anyone help?

 

[Gene]

It's the same as picking two NOT on the committee. You can pick 7*6=42 to oust. but ousting #1 then #2 is the same as #2 then #1 so you have to divide by 2. 21 ways. Or
C(7,5)=21
b correct
c) Questionable. There are 10 ways to pick the two people if they are interchangable. You are probably correct, but...
d) Same quibble. If the chairperson is picked first (1/5) then the secretary (1/4) = 1/20

c) & d) are closely related and the longer I stare at them the less sure I am which interpretation is correct. Its more an English question than math.