Question

Determine the number of arrangements of letters of the word ALGORITHM if O is the first and T is the last letter

Answer 1

In the word 'ALGORITHM' the number of letters is n = 9.

O is the first and T is the last letter:

Here, two positions for 'O' and 'T' are fixed and the remaining 7 positions are left for the remaining 7 letters.

Hence, the total number of words in which they begin with 'O' and end with 'T' = ⁷P₇ = 7!

= 7 × 6 × 5 × 4 × 3 × 2 × 1

= 5040