# In a lottery, a person choses six different natural numbers at random from1 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 games? [Hint: order of the numbers is not important.]

**Solution:**

Total number of ways in which one can choose six different numbers from 1 to 20 is ²⁰C₆

The ⁿCᵣ formula is, ⁿCᵣ = (n!) / [ (n-r)! r! ]. From this,

²⁰C₆ = (20)! / [(6)!(20 - 6)!]

= 20 × 19 × 18 × 17 × 16 × 15 × (14)! / [(6)!(14)!]

= (20 × 19 × 18 × 17 × 16 × 15) / (1 × 2 × 3 × 4 × 5 × 6)

= 38760

Hence, there are 38760 combinations of 6 numbers.

Out of these combinations, one combination is already fixed by the lottery committee.

Hence, the required probability of winning the prize in the game.

P (W) = 1/38760

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 11

## In a lottery, a person choses six different natural numbers at random from1 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 games? [Hint: order of the numbers is not important.]

**Summary:**

In a lottery, a person choses six different natural numbers at random from1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. Then the probability of winning the prize in the games is1/38760

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