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Given below are two quantities named A & B. Based on the given information; you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: Find the number of natural numbers which lie between 108 and 109 which have products of their digits as 6? Quantity B: A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?

Given below are two quantities named A & B. Based on the given information; you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: Find the number of natural numbers which lie between 108 and 109 which have products of their digits as 6? Quantity B: A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw? Correct Answer Quantity A > Quantity B

Quantity A:

108 < n < 109, n is a 9 digit number Product of 6 is possible in the following cases:

1) Exactly one digit is 6 and the remaining digits are 1:

∴ Number of possible numbers = 9

2) One digit is 2 and the other is 3, remaining are 1

∴ Number of possible numbers = 9P2 = 72

∴ Total possible numbers = 72 + 9 = 81

Quantity B:

From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that at least one black ball should be there;

We have 3 choices as given below:

Total number of ways = (When all 3 balls are black) + (2 balls are black only) + (1 ball is black only)

⇒ 3C3 + 3C2 × 6C1 + 3C1 × 6C2

⇒ 1 + 3 × 6 + 3 × 15

⇒ 1 + 18 + 45

⇒ 64

∴ Quantity A > Quantity B

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