Misc 11
In how many ways can the letters of the word ASSASSINATION be arranged so that all the Sโs are together?
Since we need to assigned 4S together,
We consider 4S as one block
So, our letters become
We arrange them now
Since letters are repeating
Hence we use this formula = ๐!/(๐1!๐2!๐3! )
Here,
n = Letters to be arranged = 9 + 1 = 10
Since 3A, 2I, 2N
p1 = 3, p2 = 2, p3 = 2,
Number of arrangements where the Sโs are together
= 10!/3!2!2!
= (10 ร 9 ร 8 ร 7 ร 6 ร 5 ร 4 ร 3!)/(3! 2! 2!)
= 151200

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.