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cgc: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Tue Jan 12, 2010 10:37 am; Thanked: 1 times

by cgc » Wed Jan 13, 2010 9:32 am

What is the best way to answer this question?

How many different 6-letter sequences are there that consist of 1 A, 2 B's, and 3 C's?

(A) 6
(B) 60
(C) 120
(D)360
(E) 720

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Source: Beat The GMAT — Problem Solving | Wed Jan 13, 2010 9:32 am

ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pmFollowed by: 1 member; Thanked: 26 times

by ace_gre » Wed Jan 13, 2010 10:40 am

Different sequences = nPr / x! * y! where x! and y! are terms that are repeated.

==>6! / (2! * 3!)
==>60, Answer is B

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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 » Wed Jan 13, 2010 7:16 pm

Different sequences = nPr / x! * y! where x! and y! are terms that are repeated.

Correction: Note that the formula for computing the total number of orders when terms are repeated is actually: n!/x!*y! where x and y are the repeated terms. (nPr is for when we are pulling out ordered subgroups of size "r" from a bigger group of size "n").

How many ways of arranging the letters in the word SLOT?

How many letters in total? 4. Any repeated letters? No. So, this is simply 4!

What about the word SLOTS?

How many letters in total? 5. But "S" shows up twice. So, this will be 5!/2!

Kaplan Teacher in Toronto

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