Probability...Help Needed!!!

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Shadow: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Thu Jun 21, 2007 9:03 pm; Location: Chennai

by Shadow » Tue Jul 10, 2007 3:04 am

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

Can you please solve this for me?...Do explain with steps...

Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Jul 10, 2007 3:04 am

givemeanid: Master | Next Rank: 500 Posts; Posts: 277; Joined: Sun Jun 17, 2007 2:51 pmFollowed by: 1 member; Location: New York, NY; Thanked: 6 times

by givemeanid » Tue Jul 10, 2007 5:16 am

For math dept, the candidate can be chosen in 7C1 different ways.
For comp dept, the two candidates can be chosen in 10C2 different ways.

So, together, the number of ways 3 candidates can be chosen = 7C1*10C2 = 7*45 = 315

So It Goes

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lanter1: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jul 05, 2007 12:53 pm; Location: Nashville

by lanter1 » Tue Jul 10, 2007 4:12 pm

perfect.

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Shadow: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Thu Jun 21, 2007 9:03 pm; Location: Chennai

by Shadow » Tue Jul 10, 2007 9:28 pm

Thanks givemeanid....

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