Question

8) Total number of words that can be formed using all letters of the word 'DIPESH' that neither with 'I' nor ends with 'D' is equal to.
(a) 504
(b) 480
(c) 624
(d) 696

Answer 1

Total number of words that can be formed using all letters of the word 'DIPESH' that neither with 'I' nor ends with 'D' is equal to.

(a) 504

To find the total number of words which neither begin with 'I' nor ends with 'D'.

First we calculate number of words formed by the 6 letters of 'DIPESH'.

It is 6!  (Total possible words)

Number of words to be excluded,

Number of words beginning with 'I' = (6-1)! = 5!

Number of words ending with 'D' = (6-1)! = 5!

Number of words beginning with 'I' and ending with 'D' = (6-2)! = 4!

∴ Remaining words = Words which neither begins with 'I' nor ends with 'D'

= 6! − (5! + 5! − 4!) = 6! −2(5!) + 4!

=720 − 240 + 24

=504

Option (A) is correct.