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Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: A box contains 3 green cubes, 5 yellow cubes and 4 blue cubes. In how many ways in which 3 cubes can be drawn so that at least 1 of the cube is yellow? Quantity B: A institute have 12 men and 8 women. 4 persons are to be selected as a volunteer in which at least 1 man is there. In how many ways can it be done?

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: A box contains 3 green cubes, 5 yellow cubes and 4 blue cubes. In how many ways in which 3 cubes can be drawn so that at least 1 of the cube is yellow? Quantity B: A institute have 12 men and 8 women. 4 persons are to be selected as a volunteer in which at least 1 man is there. In how many ways can it be done? Correct Answer Quantity A < Quantity B

Quantity A:

1 yellow and 2 others = 5C1 × 7C2 = 5 × 21 = 105

2 yellow and 1 others = 5C2 × 7C1 = 10 × 7 = 70

All the 3 yellow = 5C3 = 10

⇒ Total = 105 + 70 + 10 = 185

Quantity B:

Required no. of ways = (1 man and 3 women) + (2 men and 2 women) + (3 men and 1 women) + (4 men)

⇒ Required no. of ways = (12C1 × 8C3) + (12C2 × 8C2) + (12C3 × 8C1) + (12C4)

⇒ Required no. of ways = (12 × 56) + (66 × 28) + (220 × 8) + (495)

⇒ Required no. of ways = 672 + 1848 + 1760 + 495 = 4775

∴ Quantity B > Quantity A

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