A class has 30 students. The following prizes are to be awarded to the students of this class, first and second in Mathematics, first and second in Physics; first in Chemistry and first in Biology. If N denote the number of ways in which this can be done, then
First and second prizes in Mathematics (Physics) can be awarded in ways
First prize in Chemistry (Biology) can be awarded in ways
N is divisible by 400, 600, and 8100.
Also, N is divisible by four distinct primes numbers 2,3, 5, 29