Question

A warehouse employs 25 workers on first​ shift, 15 workers on second​ shift, and 12 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly five first​-shift workers.

Answer 1

Total workers = 25 + 15 + 12 = 52

5 first shift workers can be selected from 25 first shift workers by ²⁵C5 ways .

Where ²⁵C5 = 25! / [ ( 25 - 5)! * 5! ] = 53130

Remaining 3 workers can be selected from ( 15 + 12) = 27 workers by ²⁷C3 ways

²⁷C3 = 27! / [ ( 27 - 3)! * 3! ] = 2925

Total number of ways to select 8 workers from 52 workers by ⁵²C8

So,

⁵²C8 = 52! / [ (52 - 8)! * 8! ] = 752538150

So,

P(5 of the 8 first shift workers) = ²⁵C5 * ²⁷C3 / ⁵²C8

= 53130 * 2925 / 752538150

= 0.2065