Question

The number of permutations that can be made from the letters of the word $"SUNDAY"$ without beginning with ${}^{\prime }{S}^{\prime }$ or without ending with ${}^{\prime }{Y}^{\prime }$ is

• A. $696$
• B. $624$
• C. $604$
• D. $504$

Answer 1

Answer: (D)

$504$

Total number of permutations of the word 'SUNDAY' without any restriction is $6!$

These permutations include words that begin with S and the words that end in Y

Total number of permutations of the word 'SUNDAY' that begin with S is $5!$

Total number of permutations of the word 'SUNDAY' that end in Y is $5!$

Total number of permutations of the word 'SUNDAY' that begin with S and end in Y is $4!$

Therefore,
The required number of permutations of the word 'SUNDAY'$=6!-2\times 5!+4!=504$

Hence, answer is $504$