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joannabanana: Master | Next Rank: 500 Posts; Posts: 118; Joined: Sun Sep 05, 2010 10:21 am; Location: Canada; Thanked: 5 times; GMAT Score:730

by joannabanana » Wed Dec 01, 2010 10:48 pm

In how many ways can 11 # signs and 8* signs be arranged in a row so that no two * signs come together?

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Source: Beat The GMAT — Problem Solving | Wed Dec 01, 2010 10:48 pm

Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Thu Dec 02, 2010 12:13 am

Hi,

draw out the #s with spaces or "slots" between each of them. Then we have 10 slots. We also have a slot immediately before and immediately after the string of #s. We can place the 8 *s in any of these 12 slots. All the ways of placing 8 things into 12 spaces is the same as all the ways of "pulling out" 8 objects from 12. Thus, the answer is 12C8 (or 12C4).

Kaplan Teacher in Toronto

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