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In how many ways can the letters of the word "CALENDER" be arranged where each such letter appears exactly once?
1. 15260
2. 20160
3. 25620
4. 30840

1 Answer

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Best answer
Correct Answer - Option 2 : 20160

Given: 

The word is "CALENDER"

Concept Used:

A word having 'n' letters in which 'a' letters are repeated can be written in n!/a! ways.

n! = n(n - 1)(n - 2) ... 3.2.1. 

Where,

n = number of letters in the word

a = number of repeating letters in the word

Calculation:

According to the question, we have

The number of letters in "CALENDER" = 8

The number of letters which is repeated in the word "CALENDER" = 2

Now,

The number of ways to arrange the word "CALENDER"

⇒ 8!/2! 

⇒ (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(2 × 1)

⇒ 20160

∴ The number of ways to arrange the word "CALENDER" is 20160.

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