Question

The number of 10 digit number that can be written by using the digits 2 and 3 is …..

(a) ¹⁰C₂ + ⁹C₂

(b) 2¹⁰

(c) 2¹⁰ – 2 

(d) 10!

Answer 1

(b) 2¹⁰

Selecting the number from (2 and 3) 

For till the first digit can be done in 2 ways 

For till the second digit can be done in 2 ways … 

For till the tenth digit can be done in 2 ways 

So, total number of ways in 10 digit number = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2¹⁰