Multiple choice

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

  1. 1,00,800

  2. 72,000

  3. 45,360

  4. 40,320

  5. 30,320
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A Correct answer
Explanation

JUBILANCE has 9 letters: J, U, B, I, L, A, N, C, E. Consonants: J, B, L, N, C (5). Vowels: U, I, A, E (4). First letter can be any of 5, last any of 4. Remaining 7 letters can be arranged in 7! ways. 5 * 4 * 5040 = 100,800.

AI explanation

The word JUBILANCE has nine letters, with the consonants J, B, L, N, C and the vowels U, I, A, E. For the word to begin and end with a consonant, select two of the five consonants for the end positions and arrange them in 5P2 = 20 ways. The remaining seven letters can be arranged in the middle positions in 7! = 5040 ways. Multiplying these gives 20 * 5040 = 100800.

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