Question

All the letters of the word PADMAPRIYA are placed at random in a row. The probability that the word PRIY A occurs without getting split is ______

Options

• `1/5220`

• `1/420`

• `1/840`

• `1/329`

Answer 1

All the letters of the word PADMAPRIYA are placed at random in a row. The probability that the word PRIY A occurs without getting split is `underline(1/840)`.

Explanation:

Since there are 3 A's and 2 P's.

Total no. of arrangements = `(10!)/(3!2!)`

Hence, the number of arrangements in which PRIYA occurs without any split = `(6!)/(2!)`

∴ Required probability = `(6! 3! 2!)/(2! 10!) = 1/840`