Question

The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end with consonant is ____________.

Options

• `1/9`

• `(7!)/(9!)`

• `18/(9!)`

• `1/4`

Answer 1

The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end with consonant is `underline(1/4)`.

Explanation:

Given, word 'LOGARITHM'

Total number of arrangements = 9!

Here, vowel (O, A, I)

Consonant (L, G, R, T, H, M)

Total number of ways when starts with vowel and end with consonant is `""^3"C"_1 xx ""^6"C"_1 xx 7!`

∴ Required probability = `(""^3"C"_1 xx ""^6"C"_1 xx 7!)/(9!) = 1/4`