Question

Write all possible two digit number that can be formed by using the $3,7$and $9$ if the repetition of the digit is allowed.

Answer 1

Find the two digit number that can be formed by using the $3,7$and $9$ if the digits can be repeated.

There will be $3\times 3=9$ two digit numbers that can be formed by using the $3,7$and $9$ if the digits can be repeated.

Let us consider three cases as below:

Consider the digits $3$ and $7$ then the numbers are,

$33,37,73$ and $77$

Consider the digits $3$ and $9$ then the numbers are,

$39,93$ and $99$

Consider the numbers $7$ and $9$ then the numbers are,

$79$and $97$

Thus, all possible two-digit numbers are,

$33,37,39,73,77,79,93,97,99$

Thus, two digit number that can be formed by using the $3,7$and $9$ if the repetition of the digit is allowed are,

$33,37,39,73,77,79,93,97,99$