Answer :

Since the committee of 11 is to be formed from 6 teachers and 8 students.

(i) Forming a committee with exactly 4 teachers

Choosing 4 teachers out of 6 in ^{6}C_{4} ways.

Remaining 7 from 8 students in ^{8}C_{7} ways.

Thus, total ways in (i) are ^{6}C_{4} ^{8}C_{7} ways.

(ii) The number of ways in this case is

1. 4 teachers and 7 students

2. 5 teachers and 6 students

3. 6 teachers and 5 students

= ^{6}C_{4}^{8}C_{7}+^{6}C_{5}^{8}C_{6}^{6}C_{6}^{8}C_{5}

Applying ^{n}C_{r} =

= 344 ways

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