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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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Answer» 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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