Question

ms. bell's mathematics class consists of 6 sophomores, 14 juniors, and 10 seniors. how many different ways can ms. bell create a 5-member committee of juniors if each junior has an equal chance of being selected?

Answer 1

Answer: 2,002 different 5-member committees of juniors

Step-by-step explanation:

       We can solve this question with the given formula for combinations (since all juniors have an equal chance of being selected):

➜ n is the number of juniors

➜ r is the number of juniors in the committee

$\displaystyle _nC_r=\frac{n!}{r!(n-r)!}$

       We will substitute our known values and solve. This formula is quite simple if you substitute all the known values and compute, however, I have written out each step below so you can see how this formula works.

$\displaystyle _nC_r=\frac{n!}{r!(n-r)!}$

$\displaystyle _nC_r=\frac{14!}{5!(14-5)!}$

$\displaystyle _nC_r=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{5!(9)!}$

$\displaystyle _nC_r=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{(5*4*3*2*1)(9*8*7*6*5*4*3*2*1)}$

$\displaystyle _nC_r=\frac{87,178,291,200}{(120)(362,880)}$

$\displaystyle _nC_r=\frac{87,178,291,200}{43,545,600}$

$\displaystyle _nC_r=2,002\;\text{\;\;different\;\;committees}$

Read more about combinations here: https://brainly.com/question/28935221