Question

6 freshmen, 9 sophomores, 8 juniors, and 10 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors?
Round your answer to 6 decimal places as needed.

Answer 1

Answer: 0.027145

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Work Shown:

You will be using the nCr combination formula here. Refer to the attached image below (figures 1 through 5).

We have a pool of n = 6 freshmen and we're selecting r = 2 individuals from this pool, so there are nCr = 6C2 = 15 ways to pick the two freshmen (see figure 1).

There are 84 ways to pick the sophomores since 9 C 3 = 84 (see figure 2)

Refer to figure 3 to see how 8 C 4 = 70. So there are 70 ways to pick the juniors.

Refer to figure 4 to see how 10 C 5 = 252. There are 252 ways to pick the seniors.

Finally, refer to figure 5 to see how 33 C 14 = 818,809,200. This is the number of ways to pick 14 students from a pool of 33 (add up all the students).

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Multiply out the results of figures 1 through 4 to get:

15*84*70*252 = 22,226,400

This represents the number of ways to select all the students as mentioned in the instructions.

Then divide this over the result of figure 5

(22,226,400)/(818,809,200) = 0.02714478537858

This rounds to 0.027145 when rounding to 6 decimal places.