Question 758282: There are n men and 4 women from which a 3 person committee is to be formed. What is the probability of selecting 1 or 2 women in the group?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the probability is:
(nC2 * 4C1) / ((n+4)C3)
plus:
(nC1 * 4C2) / ((n+4)C3)
for example:
let n = 2
this means you have 2 men to choose from and 4 women to choose from which give you a total of 6 persons to choose from (2 + 4 = 6).
the number of possible combinations of getting 3 people out of 6 is equal to 6C3 which is equal to 20.
the number of ways of getting 2 men and 1 women would be equal to 2C2 * 4C1 which is equal to 1 * 4 which is equal to 4.
the number of ways of getting 1 man and 2 women would be equal to 2C1 * 4C2 which is equal to 2 * 6 which is equal to 12.
the number of ways of getting 3 women would be equal to 4C3 which is equal to 4.
if you let a,b represent the men and you let c,d,e,f represent the women, then the possible combinations are:
total of 4 ways to get 2 men and 1 woman as shown below:
a,b,c
a,b,d
a,b,e
a,b,f
total of 6 ways to get 1 man and 2 women where the man is represented by a.
a,c,d
a,c,e
a,c,f
a,d,e
a,d,f
a,e,f
total of 6 ways to get 1 man and 2 women where the man is represented by b.
b,c,d
b,c,e
b,c,f
b,d,e
b,d,f
b,e,f
total of 3 ways to get 3 women
c,d,e
c,d,f
c,e,f
remember:
men are represented by the letters a and b.
women are represented by the letters c, d, e, and f.
the probability of getting 1 woman when the number of men is equal to 2 is equal to 12/20.
the probability of getting 2 women when the number of men is equal to 2 is equal to 4/20.
the probability of getting 3 women when the number of men is equal to 2 is equal to 4/20
the total probability is equal to (12 + 4 + 4) / 20 which is equal to 20/20 which is equal to 1, as it should be.
change the value of n and the probabilities will change.
the combination formula is calculated as shown in the following example:
6C3 is equal to (6*5*4) / (3*2*1) which is equal to (5*4) which is equal to 20.
4C2 is equal to (4*3) / (2*1) which is equal to (2*3) which is equal to 6.
the general combination formula for getting x elements out of a set of n elements is:
nCx is equal to n! / ((n-x)! * x!)
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