Question

If words are formed by taking only $4$ at a time out of the letters of the word "PHYSICAL", then the number of words in which 'Y' occur is

• A. ${}^8{P}_4$
• B. $\frac{7!}{3!}$
• C. $\frac{7!}{4!}$
• D. ${}^7{C}_4$

Answer 1

The correct option is B $\frac{7!}{3!}$

'Y' can be arranged in $4$ ways and remaining $3$ letters from $7$ letters are arranged in ${}^7{P}_3$ ways.
$\therefore$ Total words formed$=4\cdot {}^7{P}_3=\frac{7!}{3!}$