Q. 14

# Out of 6 teachers

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 6C4 ways.

Remaining 7 from 8 students in 8C7 ways.

Thus, total ways in (i) are 6C4 8C7 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

= 6C48C7+6C58C66C68C5

Applying nCr =

= 344 ways

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