15-Letter Arrangements
Source:
February 20, 2008
countingdistinguishabilityAMC12
Problem Statement
How many -letter arrangements of A's, B's, and C's have no A's in the first letters, no B's in the next letters, and no C's in the last letters?
(A)\ \sum_{k\equal{}0}^5\binom{5}{k}^3 \qquad
(B)\ 3^5\cdot 2^5 \qquad
(C)\ 2^{15} \qquad
(D)\ \frac{15!}{(5!)^3} \qquad
(E)\ 3^{15}