Chapter 6 - Section 6.5 - Generalized Permutations and Combinations - Exercises - Page 433: 32

$360$

To count the number of permutations of letters of AARDVARK with the 3 A's consecutive, we can treat the 3 consecutive A's as one letter, i.e. count the number of permutations of 2 R's (indistinguishable from each other), 1 D, 1 V, 1 K, and 1 "AAA", for a total of 6 "letters". By Theorem 3 on page 428, the number of permutations is: $\frac{6!}{2!1!1!1!1!}$ $=\frac{1*2*3*4*5*6}{1*2}$ $=3*4*5*6$ $=360$