GATE ECE 2017 Set 2 | GA Question: 9

Question

The number of $3$-digit numbers such that the digit $1$ is never to the immediate right of $2$ is

• A. $781$
• B. $791$
• C. $881$
• D. $891$

Answer 1

Total Possible 3 digit number that can be formed is 900 (since we can’t place 0 in front so 9 * 10 * 10).

now given condition that 2 is in right of 1 can be satisfied if number are placed in  (x 2 1) or  (2 1 x) order. so since 9 numbers can be placed in former order and 10 in later. so answer = 900 – 10 – 9 = 881. Option C is correct.