The number of different permutations, each containing all letters of the word "STATESMAN" is

Question

The number of different permutations, each containing all letters of the word "STATESMAN" is (A) 45630 (B) 45360 (C) 45603 (D) 45600

Tardigrade Admin · Accepted Answer

"STATESMAN" Total number of letters = 9, Number of S's = 2, Number of T's = 2, Number of A's = 2 ∴ Required number of permutations = (9!/(2)! (2)!(2)!) = 45360

Q. The number of different permutations, each containing all letters of the word "STATESMAN" is

45630

45360

45603

45600

"STATESMAN"
Total number of letters = 9,
Number of S's = 2, Number of T's = 2, Number of A's = 2
$∴$ Required number of permutations
$= \frac{9 !}{( 2 )! ( 2 )! ( 2 )!} = 45360$

Q. The number of different permutations, each containing all letters of the word "STATESMAN" is

45630

45360

45603

45600

"STATESMAN" Total number of letters = 9, Number of S's = 2, Number of T's = 2, Number of A's = 2 ∴ Required number of permutations =(2)!(2)!(2)!9!​=45360

"STATESMAN"
Total number of letters = 9,
Number of S's = 2, Number of T's = 2, Number of A's = 2
$∴$ Required number of permutations
$= \frac{9 !}{( 2 )! ( 2 )! ( 2 )!} = 45360$