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  • Letter of the word INDIALOIL are arranged in all possible ways. The number of permutations in which <img alt="\mathrm{A, I, O}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7

Letter of the word INDIALOIL are arranged in all possible ways. The number of permutations in which \mathrm{A, I, O} occur only at odd places, is

Option: 1

720


Option: 2

360


Option: 3

240


Option: 4

120


Answers (1)

best_answer

\mathrm{A, I, I, I, O} can occur at odd places in \frac{5 !}{3 !} ways, and the remaining letters \mathrm{N, D, L, L} can be arranged at the remaining places in \frac{4 !}{2 !} ways.

Thus, the required number of ways = \left(\frac{5 !}{3 !}\right)\left(\frac{4 !}{2 !}\right)=240 ways

Posted by

Divya Prakash Singh

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