Question

The number of ways in which the following prizes will be given to a class of $20$ boys , first and second Mathematics , first and second Physics, first Chemistry and first English is?

• A. ${20}^4\times {19}^2$
• B. ${20}^3\times {19}^3$
• C. ${20}^2\times {19}^4$
• D. None of these

Answer 1

The correct option is A

${20}^4\times {19}^2$

Explanation for the correct option(s)

Find the number of ways.

The total number of boys in the class are $20$

The number of total first prizes to be distributed is equal to $4$

The number of total second prizes to be distributed is equal to $2$

First prizes for each of the subject can be given in $20\times 20\times 20\times 20$ ways that can be expressed as ${20}^4$

Two second prizes can be given in $19\times 19$ ways that can be expressed as ${19}^2$

As the boy cannot get both first and second prize for same subject.

Hence, required number of ways is equal to ${20}^4\times {19}^2$.

Therefore, the correct answer is Option A.