find the probability of the given event. choosing eight numbers that match eight randomly selected balls…

find the probability of the given event. choosing eight numbers that match eight randomly selected balls when the balls are numbered 1 through 38. the probability of the given event is . (type an integer or a simplified fraction.)

find the probability of the given event. choosing eight numbers that match eight randomly selected balls when the balls are numbered 1 through 38. the probability of the given event is . (type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Calculate total combinations

The number of ways to choose 8 balls out of 38 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 38$ and $r=8$. So, $C(38,8)=\frac{38!}{8!(38 - 8)!}=\frac{38!}{8!×30!}=\frac{38\times37\times36\times35\times34\times33\times32\times31}{8\times7\times6\times5\times4\times3\times2\times1}=73810801$.

Step2: Determine favorable combinations

There is only 1 favorable combination (the set of 8 numbers that match the 8 selected balls).

Answer:

$\frac{1}{73810801}$