SOLUTION: A total of 14 people - 8 men and 6 women have applied for admission to a business school. The school has 5 openings. a. How many ways are there of selecting the students to be

Question 91014: A total of 14 people - 8 men and 6 women have applied for admission to a business school. The school has 5 openings.
a. How many ways are there of selecting the students to be admitted?
b. How many ways are there if at least 4 of them must be women?
c. How many ways are there if at least 3 of them must be women?
d. How many ways if exatly 3 of them must be men?
e. How many ways if at least one of them must be a man?
Thank you all for your help. I appreciate it!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A total of 14 people - 8 men and 6 women have applied for admission to a business school. The school has 5 openings.
a. How many ways are there of selecting the students to be admitted?
14C5 = 2002 ways
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b. How many ways are there if at least 4 of them must be women?
# of ways if 4 women are selected and one man + # of ways if 5 women are selecte
= 6C4*8C1 = 120 ways
-----------------------
c. How many ways are there if at least 3 of them must be women?
6C3*8C2 + 6C4*8C1 + 6C5 = 686 ways
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d. How many ways if exatly 3 of them must be men?
8C3*6C2 = 840
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e. How many ways if at least one of them must be a man?
Answer: 8C1*6C4 + 8C2*6C3 + 8C3*6C2 + 8C4*6C1 + 8C5 = ?
I'll leave that to you.
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Cheers,
Stan H.

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