A school dance committee of 4 people is selected at random from a group of 6...

A school dance committee of 4 people is selected at random from a group of 6 ninth graders, 11 eighth graders, and 10 seventh graders. What is the probability that the committee has all seventh graders?

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Expert Solution

The probability that a committee has all seventh graders is 0.012

#################Explanation ######################

Note that here order of graders in committee does not matter.

The total number of grader :

Since there are 6 ninth graders, 11 eighth graders, and 10 seventh graders

N = 27

The total numbers of committees can form is C(27,4)

n(N) =

=17550

From 10 seven grader we can choose C(10,4) different groups of 4 seven grader

Let n(X) be the number of the committees has all seventh graders,

The number of the committees has all seventh graders

is C(10,4)

n(X) =

= 210

The probability that a committee has all seventh graders is

= 0.011965 ~0.012

The probability that a committee has all seventh graders is 0.012

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10! 4!

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C(10,4) C(27,4) 210 17550

orchestra answered 1 year ago

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