Question

Consider all possible permutations of the letters of the word ENDEANOEL. The number of permutations in which letters A. E. 0 occur only in odd positions, is ______.

Options

• 5!

• 2 × 5!

• 7 × 5!

• 21 × 5!

Answer 1

Consider all possible permutations of the letters of the word ENDEANOEL. The number of permutations in which letters A. E. 0 occur only in odd positions, is 2 × 5!.

Explanation:

There are five odd and 4 even positions. Five odd positions can be filled with A, E, E, E, O in `(5!)/(3!)` ways and four c even positions can be filled with D, N, N, L in `(4!)/(2!)` ways.

∴ require num er o permutations `(5!)/(3!) xx (4!)/(2!) = 2 xx 5!`