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Q.

The letters of the word "VICTORY" are arranged in a row at random. The probability that the vowels may be in the even places is ____

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answer is 0.1428.

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Detailed Solution

given word VICTORY

$n (S) = 7!$

E=vowels (I,O)may be in the even places

$\begin{array}{rcl} = & 1 (2) 3 (4) 5 (6) 7 \\ n (E) & = & {}^{3}{C_{2}} \times 5! \Rightarrow P (E) = \frac{{}^{3}P_{2} \times 5!}{7!} = \frac{1}{7} = 0.1428 \end{array}$

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