Find the number of permutations that can be made from the letters of the word OMEGA, if the vowels occupy odd places.

Question

P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One can travel from P to S either via Q, or via R, or via Q followed by R, respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R is

Answer 1

In the word OMEGA, the vowels O, E, and A are in odd positions.
With 3 odd positions, the vowels can be arranged in 3! = 6 ways.
The consonants M and G can be arranged in the 2 even places in 2! = 2 ways.
Therefore, the total number of permutations is \(3! × 2! = 12.\)

Find the number of permutations that can be made from the letters of the word OMEGA, if the vowels occupy odd places.

The Correct Option is A

Solution and Explanation

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