Question

A pharmaceutical company interviews 12 people for eight openings in the research department of the company. 7 of the 12 people are women. If all 12 are qualified, in how many ways can the employer fill the 8 positions if
(a) the selection is random

(b) exactly three selections are men?

plz help ASAP... I'll mark you as the brainliest!

Answer 1

Answer:

(a) 495, (b) 210

Step-by-step explanation:

Total number of persons = 12

number of openings = 8

number of women = 7

number of men = 12 - 7 = 5

(a) Number of ways to select the 8 persons

$C_{8}^{12}\textrm{}\\\\= \frac{12!}{8!\times 4!}\\\\=495$

(b) Three are men

So, 3 men and 5 women

The number of ways are

$C_{3}^{5}\textrm{} \times C_{5}^{7}\textrm{}\\\\= \frac{5!}{3!\times 2!}\times \frac{7!}{5!\times 2!}\\\\=210$