We have 7 boys and 3 girls in our church choir. there is an upcoming concert in the local town hall. unfortunately, we can only have 5 youths in this performance. this performance team of 5 has to be picked randomly from the crew of 7 boys and 3 girls. what is the probability that exactly 4 boys are picked in this team of 5?

  105/252 = 0.41666...

Step-by-step explanation:

There are (7C4)(3C1) = (35)(3) = 105 ways to choose exactly 4 boys. There are 10C5 = 252 ways to choose 5 youths, so the probability that a randomly chosen team will consist of exactly 4 boys is ...

  105/252

nCk = n!/(k!(n-k!))

There is a 41.67% probability that exactly 4 boys are picked in this team of 5.

Step-by-step explanation:

The order is not important, so we use the combinations formula.

is the number of different combinatios of x objects from a set of n elements, given by the following formula.

Number of desired outcomes.

Four boys and one girl: So

Number of total outcomes:

Combination of five from a set of 10.

So

What is the probability that exactly 4 boys are picked in this team of 5?

There is a 41.67% probability that exactly 4 boys are picked in this team of 5.

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