Answer :

Since a committee is to be formed of 2 teachers and 3 students

(i) When a particular teacher is included

No. of ways in which committee can be formed = ^{9}C_{1}^{20}C_{3}

= 9720 ways

(ii) a particular student is included

since a particular student is always selected so ways of selecting 2 teachers and 2 students from 10 and 19 respect. is = ^{10}C_{2}^{19}C_{2} ways

= 7695 ways

(iii) a particular student is excluded

since 1 particular student is excluded so , ways of selecting 2 teachers and 3 students from 10 and 19 respt. is = ^{10}C_{2} ^{19}C_{3} ways

= 43605 ways

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