Question

There are nine students ($5$ boys and $4$ girls) in the class. In how many ways
(i) One student (either girl or boy) can be selected to represent the class
(ii) A team of two students (one girl and one boy) can be selected
(iii) Two medals can be distributed (no one get both)
(iv) One prize for Maths, two prizes for Physics and three prizes for Chemistry can be distributed. (No student can get more than one prize in same subject and prizes are distinct)

Answer 1

$\left(i\right)$One student can be selected in ${}^9{C}_1$ ways =$9ways$

$\left(ii\right)$One girl and one boy can be selected in ${}^4{C}_1{\times }^5{C}_{1}ways=4\times 5=20ways$

$\left(iii\right)$Two medals can be distributed in ${}^9{C}_1{\times }^8{C}_1$ ways =$72ways$

$\left(iv\right)$ The following prizez can be distributed in ${(}^9{C}_1)\times {(}^9{C}_2)\times {(}^9{C}_3)=27216ways$