Question about probability..help needed!?

Question

We're allowed to use a graphing calculator on this, so if u can tell me just how to do this on the calculator or work it out for me, that would be good. thanks, heres the question:

There are 7 women and 4 men on a commitee. If a 4-person subcommittee is selected at random, what are the odds that it will consist of 3 men and 1 woman?

Answer 1

umm if you know how to use the combination function, then it should look like (7 nCr 3*4 nCr 1)/(11 nCr 4)

Answer 2

For Your Graphing calculator there is a function on there that uses both Permutations and Combinations, above is a combination, the formulas are nCr and nPr, to access on the calculator, hit <MATH>(under the <ALPHA> Key) and hit the right directional key over to PRB(Probability) and you will see all your probability formulas, including the two you will mainly be using.

Answer 3

4nCr1 * 3/11 * 2/10 * 1/9 * 7/8 =

4* 3*2 *7/ (11*10*9*8) = 7/ 330

Answer 4

This is a sample from the hypergeometric distribution, but it's simplest to work it out from general reasoning.

The total number of people is eleven.  The number of ways to select 4 people then is (11 choose 4).

The number of ways to select 3 out of 4 men is (4 choose 3) = 4, and we need to multiply this by the number of ways we could select the remaining woman which is (7 choose 1) = 7.

Thus, the probability that a 4 person subcommittee will have 3 men and one woman is (4 * 7)/(7 choose 1).  I'll leave you to work out the final answer on your calculator - I've never used a graphing calculator, but it should have functions for combinations and permutations.