Question

If the different permutations of all the letters of the word "examination" are listed as in a dictionary, how many words are there in this list before the first word starting with 'e'?

(a) 2,688
(b) 3,120
(c) 3,360
(d) 3,840

Answer 1

The number of words in the list before the first word starting with 'e' in the permutations of the word 'examination' is 10! = 3,840

Step-by-step explanation:

To find the number of words in the list before the first word starting with 'e', we need to determine the number of different permutations of all the letters of the word 'examination'. The word 'examination' has 11 letters in total, including 3 'i's and 2 'a's which are repeated.

Therefore, the number of permutations can be calculated using the formula N!/(n1! * n2! * ... * nk!), where N is the total number of letters and n1, n2, ..., nk represents the number of times each letter is repeated. Using this formula, the number of permutations of the word 'examination' is 11!/(3! * 2!) = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 = 66,960.

However, we only want to count the words before the first word starting with 'e', so we need to consider the permutations of the remaining 10 letters excluding the first 'e', which is 10!. Therefore, the number of words before the first word starting with 'e' is 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 =3,840.