Question

How many three digit numbers can be formed using the digits $2,3,6,7,9$ with repetition?

• A. $(5{)}^3$
• B. $(3{)}^5$
• C. $(5{)}^5$
• D. $(3{)}^3$

Answer 1

The correct option is A $(5{)}^3$

Given digits are $2,3,6,7,9.$

We have to find total number of three digit numbers formed using given digits.

Three digit number consist of three places i.e unit's, ten's and hundredth place as shown:


Unit's place can be filled in $5$ different ways using any of the given digits.

Similarly, ten's and hundredth place can also be filled in $5$ different ways using any of the given digits because repetition of digits are allowed.

So, total three digit number formed are $=5\times 5\times 5=(5{)}^3.$