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A team of conveners consisting of 4 lecturers, 4 boys and 2 girls has to be selected from 15 lecturers, 10 boys and 12 girls. In how many ways the selection can be made if the 2 lecturers who were conveners last year have to be included and 3 boys who failed in the examination cannot be chosen.

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Best answer
Lecturers Boys Girls
15 + 3 = 18 10 - = 7 12
4 - 2 = 2 4 2

∴ Number of selections = 13C2, × 7C4 × 12C2 

= 78 × 35 × 66 

= 1,80,180.

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