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