A computer programming team has 12 members. Three members are needed for a speci
ID: 3119654 • Letter: A
Question
A computer programming team has 12 members. Three members are needed for a special project.
(a) How many ways can the 3 project members be selected? Simplify your answer.
(b) Seven members of the team are women, and five are men. What is the probability that a randomly selected project team of size 3 will contain at least two women? Leave your answer in the form of a sum/product.
(c) R2D2 and C3PO are two members of the 12. How many project teams of size 3 contain R2D2 or C3PO? Leave your answer in the form of a sum/product.
Explanation / Answer
A) Total number of ways to select 3 members out of 12 is 12C3; or 12*11*10/(1*2*3);=220;
B) Total number of possibilities are 12C3=220;
Atleast 2 women means = 2 women 1 men or 3 women;
7C2*5C1 + 7C3*5C0 = 105+35 = 140;
Total probability = 140/220 = 7/11;
C) R2D2 & C3PO are also members;
total number of ways are
one is R2D2 two are normal members= 1*10C2;
One is C3PO two are normal=1*10C2;
One is R2D2 one is C3PO and one is normal member=1*1*10C1;
Total number of ways are =2*10C2+10C1=100
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