In how many different ways can the letters of the word ‘KUSUMKHERA’ be permuted?

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07 Jan 2022 ‘KUSUMKHERA’

In how many different ways can the letters of the word ‘KUSUMKHERA’ be permuted?

OPtion

1. 498960
2. 907200
3. 850062
4. 465825
5. 950020
6. 900200
7. 857200
8. 805200
9. 785000
10. None of these

Solution

The word KUSUMKHERA has 10 letters in all. The letter ‘U’ occurs 2 times, the letter ‘K’ occurs 2, and the remaining S, M, H, E, R, A each occur once.
∴ The require number of permutations
= 10! /2!2!1!1! 1!1! 1!1!
= 10! /2!2!
= (10*9*8*7*6*5*4*3*2*1)/2*2
= (10*9*8*7*6*5*2*3)
= 9,07,200

Correct Option: 2 Best Solution (1)

A.P.Singh   2 years AGO

Required numbers= 10!/(2!x2!) = 907200

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