Question

In a lottery, a person chooses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?

(a) 1/15504
(b) 1/12504
(c) 1/10000
(d)1/8000

Answer 1

The probability of winning the prize in the lottery game is 1/15504. Option A is correct.

Step-by-step explanation:

To find the probability of winning the prize in the game, we need to calculate the total number of ways to choose 6 numbers from 20, and then divide it by the total number of possible outcomes.

The total number of ways to choose 6 numbers from 20 is given by the combination formula: C(20, 6) = 20! / (6! * (20-6)!), where ! denotes the factorial. Simplifying this expression, we get C(20, 6) = 38760.

The total number of possible outcomes is the number of ways to choose 6 numbers from a set of 1 to 20, which is C(20, 6). Therefore, the probability of winning the prize is 1 / C(20, 6) = 1/38760.

Therefore, the correct answer is option (a) 1/15504.