Question

How many words can be formed from e letters of the word 'SUNDAY'? How many of these begin with D?

Answer 1

There are 6 letters in the word 'SUNDAY'. The total number of words formed with these 6 letters is the number of arrangements of 6 items, taken all at a time, which is equal to $6_{p_6}=6!$ = $6\times 5\times 4\times 3\times 2\times 1$ = 720.
If we fix up D in the beginning, then the beginning, then the remaining 5 letters can be arranged in $5_{p_5}$ = 5! ways.
So, the total number of words which begin with D = 5!
= $5\times 4\times 3\times 2\times 1$ = 120.