Question

How many ways can the letters in the word "WISCONSIN" be arranged
A. 38,572
B. 45,360
C. 69,620
D. 362,880
these are the given answers...wich one is it?

Answer 1

WISCONSIN has 9 letters, with two I's and two N's

Well, no. of ways of arranging 'n' things, with 'p' repetitions one thing among that, 'q' repetitions of another, 'r' of .... and so on is:
\[\frac{n!}{p!q!r!...}\]

so, since here you have '9' letters to arrange, and 2 repetitions each for the letter 'I' and and the letter 'N'.
\[So, ~no. ~of~~ ways = \frac{9!}{2!2!}\]

Answer 2

A. 38,572
B. 45,360
C. 69,620
D. 362,880
this are the answers that are given. wich one is it?

Answer 3

I am sorry, my solution has a mistake. (I typed it out but lost connection)

**CORRECTION** --> I missed out that WISCONSIN has 2 'S' as well.

So, now, WISCONSIN has 9 letters, with two I's and two N's and two 'S' as well.

Well, no. of ways of arranging 'n' things, with 'p' repetitions one thing among that, 'q' repetitions of another, 'r' of .... and so on is:
\[\frac{n!}{p!q!r!...}\]


so, since here you have '9' letters to arrange, and 2 repetitions each for the letter 'I' , the letter 'S' and the letter 'N':
\[So, ~no. ~of~~ ways = \frac{9!}{2!2!2!}\]