In how many ways can 4 prizes be given to 3 boys when a boy is eligible for all prizes?

Question

Philoid · Accepted Answer

Let suppose 4 prizes be P₁, P₂, P₃, P₄ and 3 boys be B₁, B₂, B₃

Now P₁ can be distributed to 3 boys(B₁, B₂, B₃) by 3 ways,

Similarly, P₂ can be distributed to 3 boys(B₁, B₂, B₃) by 3 ways,

Similarly, P₃ can be distributed to 3 boys(B₁, B₂, B₃) by 3 ways,

And P₄ can be distributed to 3 boys(B₁, B₂, B₃) by 3 ways

So total number of ways is 3 × 3 × 3 × 3 =81