# A commitee of two people is chosen at random from 5 men and 4 women,How many different Committees are possible?

A commitee of two people is chosen at random from 5 men and 4 women,How many different Committees are possible?

Could someone please explain how to this please?

### 3 Answers

- lex1028Lv 49 years agoFavorite Answer
You have 9 people to choose from

You have 9 choice for the 1st person selected

You have 8 choices for the 2nd person selected (whomever was picked 1st can't also be picked 2nd)

So there are 9 x 8 = 72 permutations

But some of those 72 are the same because order doesn't matter

Picking Ann and Bob is not different from Bob and then Ann

For each group of 2 people there are 2 ways to pick them

So you need to find how many sets of 2 are in the 72 committees(this is division)

72/2 = 36 combinations

There are 36 DIFFERENT committees

A permutation is an arrangement where different order makes it different; a combination different order is not different)

Source(s): I taught middle school math for 35 years - 4 years ago
This is not only possible, but has occured (more frequently than you would imagine). Identical twins would have the same father, as they are the result of one sperm meeting one egg and then it later divides. Fraternal twins, on the other hand, are the result of two eggs being released from the woman's ovaries and then being fertilized by two different sperm. If sperm from two different men were present, it would be possible for each egg to be fertilized by a different father. It does NOT have to occur as the result of having intercourse on the same night, either. Sperm live in the female body for up to five days, and an egg can survive for up to 24 hours after ovulation. Theoretically, you could have intercourse with someone on Monday and someone else on Saturday, and ovulate on Friday and conceive twins by two different fathers, from intercourse a week apart (even though you would ovulate the two eggs at roughly the same time).

- 9 years ago
3. MM MW WW

Doesn't matter how many people you're picking from, if there's only two people in the committee.

Unless all the people are different, in which case its a combination, picking 2 out of 9.

If there's n objects and you pick r of them, then the number of combinations is nCr which is:

{n!} over {r!(n-r)!}

Which in your case n=9 and r =2 therefore combinations = 36

Not sure which one you meant so gave both answers!