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There are 10 professors and 20 lecturers, out of whom a committee of 2 professors and 3 lecturers is to be formed. Find

Answer» (i) We have to select 2 professors out of 10 and 3 lecturers out of `20 = ""^(10)C_(2) xx ""^(20)C_(3)`
(ii) When a particular professor included `= ""^(10 -1)C_(1) xx ""^(20)C_(3) = ""^(9)C_(1) xx ""^(20)C_(3)`
(iii) When a particular lecturer included `= ""^(10)C_(2) xx ""^(19)C_(2)`
(iv) When a particular lecturer excluded `= ""^(10)C_(2) xx ""^(19)C_(3)`


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