A shipment contains 12 igneous, 10 sedimentary, and 10 metamorphic rocks. If 4 rocks are selected at random, find
the probability that exactly 2 are sedimentary.
The probability that exactly 2 of the rocks are sedimentary is
(Round to four decimal places as needed.)

2. Find number of ways to choose 2 sedimentary rocks out of 10 sedimentary rocks out of the remaining 22 non-sedimentary rocks (12 igneous + 10 metamorphic)

Number of ways to choose 2 sedimentary out of 10 sedimentary rocks=C(10,2)=45

umber of ways o choose 2 non-sedimentary out of 22 non-sedimentary rocks=C(22,2)=231

3. Multiply these two numbers together to get total number of favorable outcomes then divide by total number of possible outcomes to get probability

(C(10,2)*C(22,2))/C(32,4)

C(n,k)=n!/(k!*(n-k)!)

C(n,k) reprises the number of combinations of choosing k items from n items

C(10, 2) = 10! / (2! * (10 - 2)!)

= 45

C(22, 2) = 22! / (2! * (22 - 2)!)

= 231

C(32, 4) = 32! / (4! * (32 - 4)!)

= 35960

Now, substitute these values into the probability formula:

Probability = (45 * 231) / 35960

≈ 0.2899

A shipment contains 12 igneous, 10 sedimentary, and 10 metamorphic rocks. If 4 rocks are selected at random, find the probability that exactly 2 are sedimentary. The probability that exactly 2 of the rocks are sedimentary is (Round to four decimal places as needed.)

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A shipment contains 12 igneous, 10 sedimentary, and 10 metamorphic rocks. If 4 rocks are selected at random, find
the probability that exactly 2 are sedimentary.
The probability that exactly 2 of the rocks are sedimentary is
(Round to four decimal places as needed.)