Question

Find the number of permutations of the letters of the word STATEMENTS

Answer 1

Answer:

10! / 24 = 151200

Step-by-step explanation:

There are 10 letters, so there are 10! ways of permuting them... BUT...

we need to account for the fact that just permuting the T's among themselves is being counted as "different permutations" although they are essentially the same.

Similarly, the S's and the E's.

There are

• 3! = 6 ways of permuting the 3 T's
• 2! = 2 ways of permuting the 2 S's
• 2! = 2 ways of permuting the 2 E's

So taking these "permutations that are essentially the same" into account, the number of permutations of the letters in STATEMENTS is

10! / (3! 2! 2!)  = 10! / 24 = 5 × 6 × 7 × 8 × 9 × 10 = 151200