Question

There are 4 balls of different colours and 4 boxes of colours same as those of the balls, The number of ways in which the balls, one in each box could be placed such that a ball does not go to a box of its own colour is______ 

(a) 5 

(b) 6 

(c) 9 

(d) 12

Answer 1

Correct option: (c) 9

Explanation:

Let  B₁, B₂, B₃, B₄ → balls

A₁, A₂, A₃, A₄ → corresponding colours boxes.

B₁ wont go to A­₁. hence B₁ will go to any of A₂, A₃, A₄. if B₁ is placed in A₂, then other 3 balls can be in following 3 ways i.e.

if B₁ is placed in A₃ or A₄ we get 3 ways in each 

∴ total number of ways = 3 × 3 = 9 ways