VOLUNTEER TRAINING FOR DISADVANTAGED IN MATHS – QUESTION 16 : A committee of 6 people is to be chosen from 8 students and 6 teachers so that it contains at least 3 students and at least 2 teachers. The number of ways this can be done is – (A) 1050, (B) 1120, (C) 7560, (D) 840, (E) 2170.
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VOLUNTEER TRAINING FOR DISADVANTAGED IN MATHS – ANSWER 16 : E. Two combinations are possible, either (3 students + 3 teachers) or (4 students + 2 teachers). Number of ways = 8C3 x 6C3 + 8C4 x 6C2 = (8!) / [ (3!) (5!) ] x (6!) / [ (3!) (3!) ] + (8!) / [ (4!) (4!) ] x (6!) / [ (4!) (2!) ] = 2170. Excel language is =fact(8)/(fact(3)*fact(5))*fact(6)/(fact(3)*fact(3))+fact(8)/(fact(4)*fact(4))*fact(6)/(fact(4)*fact(2)), which is also equal to 2170.
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VOLUNTEER TRAINING FOR DISADVANTAGED IN MATHS – QUESTION 15 : A motel cleaner has 8 master keys at home to open all the rooms in a large motel. Each room can be opened by just 1 of these keys. If 40 % of the rooms are left unlocked, what is the probability that the cleaner can get into a specific room if he selects 3 keys at random before leaving home to go to work? (A) 5 / 8, (B) 5 / 16, (C) 31 / 40, (D) 3 / 20, (E) 19 / 40.
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