A committee of 5 people is to be seated from 6 men and 9 women. If the selection is made randomly what is the probability that the committee consists of 3 men and 2 women?
How do you do this problem 1) by hand+scientific calculator and 2) on graphing calculator
The answer is 240/1001
Thank you!
2007-05-26 12:34:08 · 5 answers · asked by Ms. Elisa 3 in Science & Mathematics ➔ Mathematics
There are (15 C 5) many ways to choose five people out of fifteen. Thus, this is the sample size and becomes the denominator.
The case you suggested has exactly 3 men and 2 women. Among 6 men, there are (6 C 3) many ways to choose the three men and among the 9 women, there are (9 C 2) many ways to choose the women.
Thus, the probability is expressed by:
(6 C 3) * (9 C 2) / (15 C 5)
If you have a calculator capable of solving combinatorics, then just plug in the above expression. If not:
Note that (n C r) is evaluted by n! / [r! * (n-r)!]. Therefore:
(6 C 3) = 6! / (3! * 3!) = 20
(9 C 2) = 9! / (2! * 7!) = 36
(15 C 5) = 15! / (5! * 10!) = 3003
P = 20 * 36 / 3003
P = 720 / 3003
P = 240 / 1001
2007-05-26 12:56:32 · answer #1 · answered by Eddie K 4 · 0⤊ 0⤋
I know how to do the problem by hand but not on the graphing calculator.
There are 3003 different committees that can be formed. The list below summarizes the number of possible combinations you can get from 6 men and 9 women with the different compositions of men and women that are seated.
5M ~ 6C5 = 6
4M, 1W ~ (6C4)(9C1) = 135
3M, 2W ~ (6C3)(9C2) = 720
2M, 3W ~ (6C2)(9C3) = 1260
1M, 4W ~ (6C1)(9C4) = 756
5W ~ 9C5 = 126
6+135+720+1260+756+126= 3003
Of these 3003, 720 committees have 3 men and 2 women (as shown above). Therefore the probability of having a committee with 3 men and 2 women is 720/3003 = 240/1001.
2007-05-26 20:03:19 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Total combinations of 5 people is15C5 = 3003
Total combinations of 3 men is 6C3 = 20
Total combinations of 2 women is 9C2 = 36
Probability of 3men and 2 women is 20*36 = 720
Probability = 720/3003= 240/1001
2007-05-26 19:59:32 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
the probability of choosing 3 men is 3 divided by 15 which is the total is 5 and for the women 2divided by 15 is 7.5
2007-05-26 19:45:48 · answer #4 · answered by Anonymous · 0⤊ 3⤋
Ah homework, I remember having to do this once.
2007-05-26 20:34:19 · answer #5 · answered by cerealcoyote 2 · 0⤊ 0⤋