Question

How many numbers between $100$ and $1000$ can be formed with the digits $5,6,7,8,9,$ if the repetition of digits is not allowed?

• A. $3^5$
• B. $5^3$
• C. $120$
• D. $60$

Answer 1

The correct option is D $60$

Well first off that all the numbers will be of three digits $5,6,7,8,9$

$\underset{\underset{5}{\uparrow }}{-}$ This place can be filled in $5$ ways.

$\underset{\underset{4}{\uparrow }}{-}$ After filling unit digit place we are left with $4$ nos

$\underset{\underset{3}{\uparrow }}{-}$ After filling tens and unit digit place we are left with $3$ nos.

Therefore total cases possible $=5\times 4\times 3=60$.