Multiple choice

What is the number of different words (ten-letter words) ending and beginning with a consonant which can be made out of the letters of the word ''PUNISHMENT''?

  1. 8,46,620

  2. 8,46,730

  3. 8,46,720

  4. 8,36,720

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word PUNISHMENT has 10 letters: P, U, N, I, S, H, M, E, N, T. There are 7 consonants (P, N, S, H, M, N, T) and 3 vowels (U, I, E). To start and end with a consonant, choose 2 from 7 consonants (7*6 = 42 ways). The remaining 8 letters can be arranged in 8! ways. However, the letter N repeats twice, so divide by 2!. Total = 42 * 8! / 2 = 21 * 40320 = 846720.

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