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

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21 Dec 2021 Permutation

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

OPtion

1. 37600
2. 35650
3. 37800
4. 35800
5. 34600
6. 30000
7. 29800
8. 38600
9. 36600
10. None of these

Solution

The word NANAKMATTA has 10 letters in all. The letter ‘A’ occurs 4 times, the letter ‘N’ occurs 2, letter ‘T’ occurs 2 times and the remaining two letters K & M each occur once.
∴ The require number of permutations
= 10! /4!2!2!1!1!
= 10! /4!2!2!
= (10*9*8*7*6*5*4!)/4!2*2
= (10*9*4*7*3*5)
= 37800

Correct Option: 3 Best Solution (3)

SAYAN CHATTERJEE   2 years AGO

No of ways = 10!/(2!*2!*4!)
= 37800.
Option 3.

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RAMADURAI NATESAN   2 years AGO

ans = 10! / (2!*4!*2!)=37800

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Varun   2 years AGO

10!/(4!*2!*2!)
Because 10 letters with A N T repeated respectively for 4 2 2 times

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