Question

The number of ways that all the letters of the word SWORD can be arranged such that no letter is in its original position is:

• A. $32$
• B. $44$
• C. $20$
• D. $28$

Answer 1

Answer: (B)

$44$

$SWORD$ can be arranged such that no letter is in its original position, that is all letter is wrongly positioned (De arrangement)
De-arrangement formula is $n!(1-\frac{1}{1}+\frac{1}{2!}-\frac{1}{3!}+.....(-1{)}^n\frac{1}{n!})$
In this case $n$$=5$
Number of ways is $\frac{5!}{2!}-\frac{5!}{3!}+\frac{5!}{4!}-1=44$