Math probabilty help?

Count the total number of groups:

9 choose 5 = 9*8*7*6/(4*3*2*1) = 9*2*7 = 126.

b) Count the number of groups where 3 women where chosen and 2 men.

(4 choose 3) * (5 choose 2) = 4 * 10 = 40.

The prob that a random committee has exactly 3 women = 40/126

c) If there were no women then the number of ways this can happen is:

(4 choose 0) * (5 choose 5). As you could probably already see, there is only 1 way to have a committe of 5 men and 0 women. The prob = 1/126.

f) >=3 women is the same as saying 3 or 4 women as 4 women is the most you can have.

(4 choose 3)*(5 choose 2) + (4 choose 4) * (5 choose 1)=

4*10 + 1*5 = 45. Prob = 45/126.

Your question is missing a very important part to determine probability.

How many do you want in your group? If you don't give that information, the question is open to interpretation.

I'm going to do a little explaining, and try to solve the problem yourself.

1. Separate the problem into 2 sets that don't intersect (what is in one set doesn't exist in the other)

For this problem the 2 sets are obviously Men and Women. If you're one, you aren't considered in the other.

2. Determine how many of each set you want. Both sets should have a number even if it's zero.

3. Determine if order is important in how a choice is made. If it's important, use Permutations, if not use Combinations.

Say you want a group of 4 people where exactly 3 are women.

Separate into groups.

1. Men, Women.

2. How many we want from each group. To get exactly 3 women, we want exactly 1 man.

Men: 1, Women: 3

3. Order of selection is not important.

use Combination.

C(5,1) * C(4,3) will be the numerator of your probability.

Where

C(5,1) Means I have 5 men total, and I want exactly 1.

C(4,3) Means 1 have 4 women total and I want exactly 3.

We multiple these two to get the total possible.

The denominator is simply group everything together. we want 4 people out of 9

C(9,4)

Try doing the other two yourself.

Part of your question is missing. Read it again. A group of five men and four women cannot suddenly "become" any of the options you give without first picking a number of them at random. How many was it you were supposed to pick?

in a 5 men and 4 women.

if 3 person is outcome then;

I-1 man and 2 women,

II-2 men and 1 woman,

III-at least 3 men.

IV-at least 3 women.

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F