Question

How many $3$ digit numbers can be made using all the even digits between $1$ to $9$?

• A. $24$
• B. $60$
• C. $120$
• D. $360$

Answer 1

The correct option is A $24$

There are $4$ even numbers between $1$ to $9$ i.e $2,4,6,8.$

Now, we have to find all the three digit numbers formed by using these even digits.
This can be observed as arrangement of $4$ different things taken $3$ at a time, which is equal to ${}^4{P}_3.$
$\Rightarrow {}^4{P}_3=\frac{4!}{(4-3)!}=\frac{4!}{1!}=24.$