Question

in a lottery, the top cash prize was $668 million, going to three lucky winners. players pick four different numbers from 1 to 56 and one number from 1 to 41. a player wins a minimum award of $375 by correctly matching three numbers drawn from the white balls (1 through 56) and matching the number on the gold ball (1 through 41). what is the probability of winning the minimum award?

Explanation:

Step1: Calculate number of ways to choose white - balls

The number of ways to choose 4 different numbers from 56 white - balls is given by the combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 56\) and \(r=4\). So, \(C(56,4)=\frac{56!}{4!(56 - 4)!}=\frac{56\times55\times54\times53}{4\times3\times2\times1}=366150\).

Step2: Calculate number of ways to choose gold - ball

The number of ways to choose 1 number from 41 gold - balls is \(C(41,1)=\frac{41!}{1!(41 - 1)!}=41\).

Step3: Calculate total number of possible combinations

The total number of possible combinations of choosing 4 white - balls and 1 gold - ball is the product of the number of ways to choose white - balls and the number of ways to choose gold - ball. So, the total number of combinations \(N = C(56,4)\times C(41,1)=366150\times41 = 15019150\).

Step4: Calculate probability of winning

Since there is only 1 winning combination, the probability \(P\) of winning the minimum award is \(\frac{1}{15019150}\).

Answer:

\(\frac{1}{15019150}\)