Q36 / 100 · BITSAT 2024 (Memory Based Paper 1) · Mathematics

The number of arrangements of all digits of 12345 such that at least 3 digits will not come in its position is

  • A
    $89$
  • Correct answer
    B
    $109$
  • C
    $78$
  • D
    $57$

Solution

Total number of ways such that at least 3 digits will not come in its position $={ }^5 C_3\left\{3!-{ }^3 C_1 2!+{ }^3 C_2 1!-{ }^3 C_3 0!\right\}$ $+{ }^5 C_4\left\{4!-{ }^4 C_1(3!)+{ }^4 C_2(2!)-{ }^4 C_3(1!)+{ }^4 C_4\right.(0!)\}$ $+{ }^5 C_4\left\{5!-{ }^5 C_1 4!+{ }^5 C_7 3!-{ }^5 C_2 2!+{ }^5 C_4 1!-\right.\left.{ }^5 C_5(0!)\right\}$ $=10(2)+5(9)+(44)=20+45+44=109$

Hence, the correct answer is option: 'B'.

Relevant Questions