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The number of permutations of the letters of the word EXERCISE

Question

The number of permutations of the letters of the word EXERCISES taken 5 at a time is

2250

30240

22660

None of these

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The number of permutations of the letters of the word EXERCISES taken 5 at a time is

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Text solutionVerified

Given word is

EXERC I SES

Hence

E^{'} s = 3

S^{'} s = 2

Hence the required combination is
the coefficient of

x^{5}

5! [(1 + x + \frac{x ^{2}}{2 !} + \frac{x ^{3}}{3 !}) (1 + x + \frac{x ^{2}}{2 !}) (1 + x)^{4}]

Simplifying , we get the coefficient as

10 (36 + 96 + 72 + 21)

= 10 \times 225

= 2250

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Question Text	The number of permutations of the letters of the word EXERCISES taken 5 at a time is
Answer Type	Text solution:1
Upvotes	150