Question
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
BITSAT
Mathematics
Permutation Combination
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. ^7 C_2 2^5
- B. ^7 p_2 2^5
- C. ^7 C_2 5^2
- D. None of these
Answer
A. ^7 C_2 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 C_2. Hence, the required number of ways is ^7 C_2 2^5.
Related: Mathematics — Permutation Combination · All PYQ Banks