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Mathematical Skills | Permutation and Computation

 Q. No. 1: A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 women. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed? A : 3724 B : 3630 C : 4914 D : 3824 Solution
 Q. No. 2: For a GPLassets, a selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Dishant is selected, Gautam and Jitendra will not be selected and vice-versa. In how many ways it can be done? A : 572 B : 672 C : 472 D : 372 Solution
 Q. No. 3: In how many ways can a leap year have 53 Sundays? A : 365C7 B : 7 C : 4 D : 2 Solution
 Q. No. 4: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert. A : 252 B : 240 C : 300 D : 340 Solution
 Q. No. 5: A 6x6 grid is cut from an 8x8 chessboard. In how many ways can we put two identical coins, one on the black square and one on a white square on the grid, such that they are not placed in the same row or in the same column? A : 216 B : 324 C : 144 D : 108 Solution
 Q. No. 6: There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person? A : 35 B : 70 C : 105 D : 210 Solution
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