Question

In a certain college at the B.Sc. examination, in each subject Physics, Chemistry and Maths there are $3$ students getting honours, no candidates obtaining honours in more than one subject; Find the number of ways in which 9 scholarships of different value be awarded to the $9$ candidates if due regard is to be paid only to the places obtained by candidates on any one object.

Answer 1

3 candidates obtained first class honours in maths, physics and chemistry.

No candidates obtain honours in more than one subject.

we have to find no. of ways in which 9 scholarships of different value awarded to 9 candidates, if due regard is to be paid only to the places obtained by candidates in any one subject.

Now No. of ways giving scholarship in Math $=3!$

Similarly in physics and chemistry, no. of ways $=3!$

Total scholarship $=9$

Required No. of ways $=\frac{9!}{3!3!3!}$

$=1680$