Question

Find the number of ways in which a committee of 2 teachers and 3 students can be formed out of 10 teachers and 20 students. In how many of these committees a particular teacher is included?

Answer 1

Number of ways a committee of 2 teachers and 3 students can be formed out of 10 teachers and 20 students.

${=}^{10}{\text{C}}_2{\times }^{20}{\text{C}}_3$

$=45\times \frac{20\times 19\times 18}{3\times 2\times 1}$

$=51300$ ways

when partivular teacher is included

${=}^9{\text{C}}_2{\times }^{20}{\text{C}}_3$

$=9\times \frac{20\times 19\times 18}{3\times 2\times 1}$

$=10260$ ways