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Perms + Combination 2

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Intern
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Joined: 06 May 2012
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Perms + Combination 2 [#permalink] New post 20 May 2012, 12:21
There are 5 women and 3 men in the board of XYZ company. In how many ways can a three-people committee be formed if at least 1 man must be included in the committee?
a)10
b)18
c)46
d)56
e)63

Please help me to solve this problem. Thks!!
Director
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Joined: 24 Jul 2011
Posts: 504
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
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Kudos [?]: 159 [0], given: 9

Re: Perms + Combination 2 [#permalink] New post 20 May 2012, 18:04
Case 1: 1 man, 2 women => 3C1 x 5C2 = 30 ways
Case 2: 2 men, 1 woman => 3C2 x 5C1 = 15 ways
Case 3: 3 men, no women => 3C3 = 1 way

Total number of ways to form the committee = 30 + 15 + 1 = 46 ways

Option (C)
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Re: Perms + Combination 2   [#permalink] 20 May 2012, 18:04
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