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In how many ways first and second rank i...

In how many ways first and second rank in mathematics, first and second rank in physics, first rank in chemistry, and first rank in English be given away to a class of 30 students.

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The correct Answer is:
`(30xx29)xx(30xx29)xx30xx30`
First and second prizes can be given in Mathematics in `(30xx29)` ways.
First and second prizes can be given in Physics in `(30xx29)` ways.
First prize can be given in Chemistry in 30 ways.
First prize can be given in English in 30 ways.
Hence, the number of ways to give prizes in all the four subjects.
`=(30xx29)xx(30xx29)xx30xx30`
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