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Permutation and Combination


A cat show is featuring six different cats. Two are Persians, two are Siamese, and two are Burmese. How many ways can the organizer arrange the cats if all the cats of the same breed are to stand next to each other?

A. 10
B. 22
C. 48
D. 60
E. 74

Answer

The formula for a permutation is: nPr= n!/(n-r)! where n is the total number of selections available and r is the number of items to be selected.

From the permutation formula with n equal to 2 and r equal to 2 this results in: 2P2= 2! = 2.

Since there are 6 ways to arrange the groups and 8 ways to arrange the cats within their own groups there are 8X6 or 48 different ways to arrange the models.

Correct Answer - Choice C


GMAT Permutation and Combination - Dividing Objects into GroupsDivision of Objects into Groups: The GMAT sometime tends to surprise test-takers with questions on little-known topics. Although the topic of combinations is a widely known and studied topic, a sub-topic within combinations that is sometimes neglected by a significant number of test takers is that of division of objects into groups.

The number of ways to divide m+n+p objects into three groups having m,n, and p objects is (m+n+p)!/(m! n!  p!)

Example: In how many ways can you divide 28 schoolchildren into three groups having 3,5, and 20 children?

Solution: The answer is simply 28!/(3!5!20!)

This problem type is simple enough. However, the GMAT can try to trick you by asking you a subtle variant of this type of problem.

The number of ways to divide m+2n objects into three groups having m,n, and n objects is (m+2n)!/m! x n! x n! x (no. of groups having the same number of objects)!

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