Question

If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.

Answer 1

In a dictionary the words at each stage are arranged in alphabetical order. In the given problem we must therefore consider the words beginning with A, E, L, T in order.

'A' will occur in the first place as often as remaining 3 letters all at a time i.e, A will occur in the first place the same number of times.

$\therefore$ Number of words starting with A = 3!
=6

Number of words starting with E = 3! = 6

Number of words begining with L is 3!, but one of these words is the word LATE itself.

$\therefore$ Rank of LATE = 2 $\times$ 6 + 2

= 12+2

= 14.