Question

How many numbers have exactly 3 digits when expressed in either bases 5 or 11?

Answer 1

Answer:

consonant 5 or 11

Step-by-step explanation:

because 15, 30 that's why 5 consonant.

because 33,66 that's why 11 consonant.

Answer 2

For Base 5  the number of 3-digits $= 180$

For Base 11 the number of 3-digits $= 1584$

Explanation:

For Base 5

Number of ways to fill the left most place is 5 excluding "0" , since it is 3-digits number.

other 3 places can be fill with 6 different digits

Hence,     $5\times6\times6 = 180$

For base 11

Number of ways to fill the left most place is 11 excluding "0" , since it is 3-digits number .

other 3 places can be fill with 11 different digits

Hence,   $11\times12\times12 = 1584$ .