A retail company must choose a few employees to send to a na

A retail company must choose a few employees to send to a national retail conference. Of the 717 employees at this company, 467 are male.If 5 employees are randoomly chosen, find the probability that exatcly 4 are male

Solution

5 employees can be choosen from 717 employees in ⁷¹⁷C₅ ways = 717! / (5! * 712!)

= (717 * 716 * 715 * 714 * 713 ) / (5* 4* 3* 2*1) = 186864137820360/120 = 1557201148503 ways

Out of 717 employees 467 are males and rest are females i.e 717 - 467 = 250 females

Out of 5 randomly selected employees if exactly 4 are males then 1 will be female = ⁴⁶⁷C₄ * ²⁵⁰C₁

   = (467! / 4! * 463!) *( 250! / 249! * 1!)

= (467 * 466 * 465 * 464 /4 *3*2) * (250)

= 1956421780 * (250) = 4.89105445 * 10¹¹

Therefore probability that exactly 4 males are selected =4.89105445 * 10¹¹ / 1557201148503

= 0.314093