Question

How many $10$-digit numbers can be written by using digits $9$ and $2$?

• A. ${}^{10}C_1+{}^{9}C_2$
• B. $2^{10}$
• C. ${}^{10}C_2$
• D. $10!$

Answer 1

The correct option is B

$2^{10}$

To find the total numbers:

Each digit of the number can have two digits $9$and $2$

Thus we can fill each digit in $2$ways.

Therefore, the total number of $10$-digit numbers$=2\times 2\times ...\times 2(10times)$

$=2^{10}$

Hence the correct option is B.