A Scrabble player has the six letters (A, A, E, E, N, N) in her rack. How many distinguishable, six-letter permutations can be formed?
A) 90
B) 240
C) 360
D) 720

Question

Quizplus · Accepted Answer

The number of distinguishable permutations of the letters can be calculated using the formula for permutations of multiset: n! / (n1! * n2! * ... * nk!), where n is the total number of letters, and n1, n2, ..., nk are the frequencies of the distinct letters. Here, n = 6, and the frequencies are 2 A's, 2 E's, and 2 N's. So, the number of permutations is 6! / (2! * 2! * 2!) = 720 / 8 = 90.

A Scrabble Player Has the Six Letters (A, A, E