Question

In how many ways 6 prizes can be distributed among 10 students in the following manner: 3 in Mathematics, 2 in Physics and 1 in Chemistry?

• A. 10⁶
• B. 6¹⁰
• C. 10³.9².8
• D. 8.³9².10

Answer 1

Answer: (C)

10³.9².8

Answer 2

First, second and third prize in Mathematics can be given in 10, 9 and 8 ways (Note that one who takes first prize of Mathematics cannot receive 2^nd in the same).

Similarly 1^st, 2^nd prize in Physics and 1^st in Chemistry can be given is 10, 9 and 10 ways respectively.

∴ Total ways = 10 x 9 x8 x 9 x 10 x 10 = $10^{3}9^{2}8$.