How many distinct arrangements of the letters in the word football are possible?
A) 10,080
B) 1680
C) 720
D) 40,320

Question

Quizplus · Accepted Answer

The word "football" has 8 letters with "o" repeated twice and "l" repeated twice. The formula for arrangements with repeated letters is n! / (p1! * p2! * ... * pk!), where n is the total number of letters, and p1, p2, ..., pk are the frequencies of each repeated letter. Here, it's 8! / (2! * 2!) = 40,320 / (2 * 2) = 10,080.

How Many Distinct Arrangements of the Letters in the Word