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