Question

How many numbers lying between $100$ and $1000$ can be formed with the digits $1,2,3,4,5$ if the repetition of digits is not allowed -

• A. $62$
• B. $60$
• C. $64$
• D. $65$

Answer 1

The correct option is B $60$

Solution :-

number lying between 100 and 1000

formed by 3 digits.

and every digit have 5 option (1,2,3,4,5)

to select a number

But repetion is not allowed

so number = ${}^5{P}_3$

$=\frac{5!}{(5-3)!}$

$=\frac{5!}{2!}$

$=60m.$