In a lottery, a person choses 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. [Hint order of the numbers is not important.]

Explanation

The given number of numbers present in the lottery is equal to 6.

The set of numbers from which the given 6 numbers can be chosen is equal to
`1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20`.

The total numbers in the given set is equal to 20.

The number of ways of choosing 6 numbers from the given set of 20 numbers
= 20C6

We know that `nCr=n!r!(n−r)!
and n!=n(n−1)(n−2).....2×1`

By applying the above formula, we get

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