Question

Number of words that can be made with the letters of the word ''GENIUS" if each word neither begins $G$ and nor end with $S$

• A. $24$
• B. $240$
• C. $480$
• D. $504$

Answer 1

Answer: (D)

$504$

Consider the given question,

The number of words that can be made with "GENIUS" if letters neither begin with G and nor ends in S.

Number of letters in "GENIUS" is $6!$

If we exclude G as starting letter then a number of letters are $5!$

If we exclude S as the ending letter is $5!$

Now, the number of letters remaining letters starting with G and ending S are $4!$

Therefore,

Total number of letters that can be formed

$6!+4!-5!-5!$

$=720+24-120-120$

$=744-240$

$=504$

Hence, the number of words that can be made with "GENIUS" if letters neither begin with G and nor ends in S is $504$.