Solve the problem.
-How many ways can the letters in the word ʺWISCONSINʺ be arranged?
A) 38,572
B) 69,620
C) 362,880
D) 45,360

Question

Quizplus · Accepted Answer

The word "WISCONSIN" has 9 letters with the following repetitions: I (2 times), S (2 times), and N (2 times). The formula for permutations of a set of objects where some objects are indistinguishable is n! / (p1! * p2! * ... * pk!), where n is the total number of objects, and p1, p2, ..., pk are the numbers of objects that are identical. Here, n = 9, and we have three sets of identical letters (I, S, N), each set having 2 identical letters. Thus, the number of arrangements = 9! / (2! * 2! * 2!) = 362,880 / (2 * 2 * 2) = 362,880 / 8 = 45,360.

Solve the Problem. -How Many Ways Can the Letters in the Word ʺWISCONSINʺ