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Find the number of ways in which a commi...

Find the number of ways in which a committee of 11 members can be formed out of 6 teachers and 8 students if there are at least 4 teachers in the committee.

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The committee can be formed in the following ways:
(i) 4 teacher +7 students
No. of ways of selection `= .^(6)C_(4) xx ^(8)C_(7)`
(ii) 5 teachers +6 students
No. of ways of selection `= .^(6)C_(5) xx ^(8)C_(6)`
(iii) 6 teacher +5 students
No of ways of selection `= .^(6)C_(6) xxe^(8)C_(5)`
The committee can be formed in any one way, therefore from addition principle
Required ays `= .^(6)C_(4) xx^(8)C_(7) +^(6)C_(5)xx^(8)C_(6) +^(6)C_(6) xx^(8)C_(5)`
`= 15 xx 8 +6 xx 28 +1 xx 56`
`=120 +168 +56`
`= 344`.
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