First slide
Permutations
Question

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

Moderate
Solution

First and second prizes in Mathematics (Physics) can be awarded in  30P2 30P2= 30P22=(30)2(29)2 ways

First prize in Chemistry (Biology) can be awarded in  30P1 30P1=(30)2 ways 

Hence 

N=(30)2(29)2(30)2=(30)4(29)2=243454292

since ,400=2452,600=23352,8100=223452

N is divisible by 400, 600, and 8100. 

Also, N is divisible by four distinct primes numbers 2,3, 5, 29

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