Question

In one​ lottery, a player wins the jackpot by matching all five numbers drawn from white balls​ (1 through 45​) and matching the number on the gold ball​ (1 through 35​). If one ticket is​ purchased, what is the probability of winning the​ jackpot?

Answer 1

Answer:

the probability of winning the​ jackpot is 1 in 42 761 565.

Step-by-step explanation:

The number of ways to select five numbers from 45 is:

ⁿCₐ = n! / (n - a)! × a!

where

• a is the number of objects
• n is the number of distinct objects

Therefore,

⁴⁵C₅ = 45! / (45 - 5)! × 5!

      = (45 × 44 × 43 × 42 × 41) / (5 × 4 × 3 × 2 × 1)

      = 1221759

There are 35 ways to select a gold ball. Therefore, the total number of ways to get 6 matching numbers is:

1221759 × 35 = 42 761 565