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

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

Infinity Learn · Accepted Answer

First and second prizes in Maths and Physics can be  awarded in   $$30P2.30P2=(30P2)2$$      ways  First prize is Chemistry, Biology can be awarded in $$=30.30=(30)2$$      ways  ∴      $$N=(30P2)2$$.$$(30)2=304.292=24.34.54.292$$       As $$400=24.52$$, $$600=23.3.52$$, $$8100=22.34.52$$,       We get N is divisible by each of $$400$$, $$600$$, $$8100$$       and also N is divisible by $$4$$ primes $$2$$, $$3$$, $$5$$, $$29$$

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

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