Question

The number of words that can be made by arranging the letter of the word ROORKEE that neither begin with r nor end with e

Answer 1

Number of choices for first letter (r) = 2
number of choices for last letter (e) = 2
so total number of ways = 2x2 x 5!/ 2! = 240
number of ways of arranging 7 letters with no conditions = 7!/2!x2!x2!=630
neither start with r nor end with e = total - (start with r and ends with e)
= 630 - 240
= 390