Question

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is …..

(a) 30⁴ × 29² 

(b) 30³ × 29³ 

(c) 30² × 29⁴ 

(d) 30 × 29⁵

Answer 1

(a) 30⁴ × 29² 

I and II in maths can be given can be given in 30 × 29 ways. 

I and II in physics can be given in 30 × 29 ways. 

I and chemistry can be given in 30 ways. 

I in English can be given in 30 ways. 

So total number of ways = 30 × 29 × 30 × 29 × 30 × 30 = 30⁴ × 29²