Mathematics: Aclass committee is to be made that consists of 2 freshmen, 2 sophomores, 3 juniors, and 3 seniors. if students are being randomly chosen from groups of 12 freshmen, 17 sophomores, 16 juniors, and 20 seniors, how many possible committees can be formed?

Aclass committee is to be made that consists of 2

Ответ:

Elenegoggg

12.03.2022

Freshmen: ₁₂C₂ $\frac{12!}{2!(12 - 2)!} = \frac{12!}{2!*10!} = \frac{12 * 11 * 10!}{2*10!} = \frac{12 * 11}{2} = 6 * 11 = 66$

Sophomore: ₁₇C₂ = $\frac{17!}{2!(17 - 2)!} = \frac{17!}{2!*15!} = \frac{17 * 16 * 15!}{2 * 15!} = \frac{17 * 16}{2} = 17 * 8 = 136$

Juniors: ₁₆C₃ = $\frac{16!}{3!(16 - 3)!} = \frac{16!}{3!*13!} = \frac{16 * 15 * 14 * 13!}{3 * 2 * 13!} = \frac{16 * 15 * 14}{2 * 3} = 8 * 5 * 14 = 560$

Seniors: ₂₀C₃ = $\frac{20!}{3!(20 - 3)!} = \frac{20!}{3!*17!} = \frac{20 * 19 * 18 * 17!}{3*2*17!} = \frac{20 * 19 * 18}{2 * 3} = 10 * 19 * 6 = 1140$

₁₂C₂ * ₁₇C₂ * ₁₆C₃ * ₂₀C₃

66 * 136 * 560 * 1140 = 5,730,278,400

5,730,278,400

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Ответ:

vdavihbk

12.03.2022

Mathematics

$C(12,2)\cdotC(17,2)\cdotC(16,3)\cdotC(20,3)=\\\\\dfrac{12!}{2!10!}\cdot\dfrac{17!}{2!15!}\cdot\dfrac{16!}{3!13!}\cdot\dfrac{20!}{3!17!}=\\\\\dfrac{11\cdot12}{2}\cdot\dfrac{16\cdot17}{2}\cdot\dfrac{14\cdot15\cdot16}{2\cdot3}+\dfrac{18\cdot19\cdot20}{2\cdot3}=\\\\66\cdot136\cdot560\cdot1140=5,730,278,400$

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Ответ:

bommers144

14.08.2020

Mathematics

9514 1404 393

(0, 0), (3, 5)

Step-by-step explanation:

When the graph represents direct variation, it passes through the origin (0, 0) and any points that have the same y/x ratio. Here, that ratio is 10/6 = 5/3, so points like (3, 5) and (9, 15) will be on the graph.

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Aclass committee is to be made that consists of 2 freshmen, 2 sophomores, 3 juniors, and 3 seniors. if students are being randomly chosen from groups of 12 freshmen, 17 sophomores, 16 juniors, and 20 seniors, how many possible committees can be formed?

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