Question

Sujoy is putting up his paintings for an art gallery. Out of $5$ of his best paintings, he has to arrange any $2$ on the wall dedicated to him.

• A. $10$
• B. $20$
• C. $16$
• D. $25$

Answer 1

The correct option is B $20$

Here order matters and repetition is not allowed because each painting only exists once.

For the first part he is having $5$ choices and for other part he is having $4$ choices

Using counting, number of ways to arrange $2$ paintings
$=5\times 4=20$

Using permutations, number of ways to arrange $2$ paintings
$={}^5{P}_2=\frac{5!}{(5-2)!}$
$=\frac{5\times 4\times 3!}{3!}$
$=5\times 4=20$