Solve.
-In how many distinguishable ways can the letters of the word WINDOW be arranged?
A)120
B)720
C)360
D)36

Question

Quizplus · Accepted Answer

The word WINDOW has 6 letters with the letter W repeated twice. The formula for permutations of n items with repetitions is n! / (n1! * n2! * ... * nk!), where n! is the factorial of n, and n1!, n2!, ..., nk! are the factorials of the counts of each repeating item. Here, n = 6 (for the six letters in WINDOW), and we have one repeating letter (W) occurring twice. Thus, the number of distinguishable arrangements is 6! / 2! = 720 / 2 = 360.

Solve. -In How Many Distinguishable Ways Can the Letters of the the Word