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

(i) a particular teacher is included?


(ii) a particular student is included?


(iii) a particular student is excluded?


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 = 9C120C3


= 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 = 10C219C2 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 = 10C2 19C3 ways


= 43605 ways


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