BITSAT2022MathematicsPermutation and CombinationActual
The number of different seven-digit numbers that can be written using only the three digit 1 , 2 and 3 with the condition that the digit 2 occurs twice in each number is
Options
- A^7 C₂ 2^5
- B^7 p₂ 2^5
- C^7 C₂ 5^2
- DNone of these
Correct answer
A. ^7 C₂ 2^5
Step-by-step solution
Other than 2, remaining five places can be filled by 1 and 3 for each place. The number of ways for five places is 2 2 2 2 2=2^5 . For 2 , selecting 2 places out of 7 is ^7 C₂ . Hence, the required number of ways is ^7 C₂ 2^5 .