Find the number of ways in which the letters of word taurus be arranged using all the letters

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80 Questions 80 Marks 45 Mins

Concept:

If we subtract the arrangements in which all 3 ‘E’ come together from total arrangement then we will get the required arrangements.

Formula used:

Arrangement of n letters of a word if no two letters repeat itself = n!

Arrangement of n letters of a word if a word repeats itself x times = n!/x!

Calculation:

In word “SENTENCE” letter ‘E’ repeats 3 times and Letter ‘N’ repeats 2 times

So total possible arrangement = 8!/(3! × 2!)

Arrangement in which all 3 ‘E’ comes together = 6!/2!

Now the required arrangement = 8!/(3! × 2!) – 6!/2! = 3360 - 360 = 3000

∴ Required arrangement = 3000 

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