Question

How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N. How many begin with N and end in Y ?

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 N in the begining, then the remaining 5 letters can be arranged in $5_{p_5}5!$ ways so, the total number of words which begin with N = 5! =$5\times 4\times 3\times 2\times 1=120$ If we fix tip N in the beginning and Y at the end, then the remaining 4 letters can be arranged in $4_{P_4}$ 4! ways. So, the total number of words which begin with N and end with Y 4! =$4\times 3\times 2\times 1$= 24.