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 $={ }^{9} \mathrm{C}_{1} \times{ }^{20} \mathrm{C}_{3}$
= 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 $={ }^{10} \mathrm{C}_{2} \times{ }^{19} \mathrm{C}_{2}$ 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 $={ }^{10} \mathrm{C}_{2} \times{ }^{19} \mathrm{C}_{3}$ ways
= 43605 ways