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Eduardwww [97]
3 years ago
6

Suppose you are going to form a committee of students and faculty. You have 10 total students and 11 total faculty to pick from.

You want to have 9 total people on the committee. What is the probability that you select 3 students and 6 faculty, in that order? Enter your answer rounded to three decimals.
Mathematics
1 answer:
zlopas [31]3 years ago
3 0

Answer:

0.189

Step-by-step explanation:

We are using combination to solve for this.

C(n,r) = nCr = n!/r! (n - r)!

We have 10 total students and 11 total faculty = 21 people

Step 1

Selecting 3 students out of 10 total students

= 10× 9× 8×7×6×5×4×3×2×1/ 3×2×1 × 7×6×5×4×3×2×1/

= 120

Step 2

Select 6 faculty out of 11 faculty

11C6 = 11!/6!(11 - 6)!

= 11!/6! × 5!

= 11×10× 9× 8×7×6×5×4×3×2×1/6×5×4×3×2×1 × 5×4×3×2×1/

= 462

Step 3

Selecting 9 people out of 21 people to form a committee

21C9 = 21!/9!(21 - 9)!

= 21!/9! × 12!

= 293,930

Step 4

The fourth and final step of having a committee of 9 people =

(120 × 462)/293,930

= 55440/293,930

= 0.1886163372

Rounded to 3 decimal places = 0.189

Therefore, the probability that you select 3 students and 6 faculty = 0.189

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