Question
The number of arrangements of all digits of 12345 such that at least 3 digits will not come in its position is
BITSAT
Mathematics
Permutation Combination
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 89
- B. 109
- C. 78
- D. 57
Answer
B. 109
Step-by-step solution
Total number of ways such that at least 3 digits will not come in its position = ^5 C_3 \ 3!- ^3 C_1 2!+ ^3 C_2 1!- ^3 C_3 0! \ + ^5 C_4 \ 4!- ^4 C_1(3!)+ ^4 C_2(2!)- ^4 C_3(1!)+ ^4 C_4 .(0!)\ + ^5 C_4 \ 5!- ^5 C_1 4!+ ^5 C_7 3!- ^5 C_2 2!+ ^5 C_4 1!- . . ^5 C_5(0!) \ =10(2)+5(9)+(44)=20+45+44=109
Related: Mathematics — Permutation Combination · All PYQ Banks