Question

Question 11 In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

Class X1 - Maths -Permutations and Combinations Page 157

Answer 1

Here Letters in given word:
A S S A S S I N A T I O N
A -3 times
S -4 times
I -2 times
T -1 times
O -1 times
N -2 times

If all S's are together ,then it will be considered as 1 letter and remaining (13-4) = 9 letters and 1 S ( including 4S's) will be considered as 10 letters .

Hence, total number of ways = 10!/3!×2!×2! [ because 3 times of A, 2 times of I and 2 times of N}
= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3!/3!×2!×2!
= 10 × 9 × 8 × 7 × 6 × 5
= 151200 ways .