Question

Find the probability that the employer gives vacation hours to 3 males and 3 females if she chooses 6 students from the class at random.

Answer 1

This question is incomplete, the complete question is;

An employer has a total of 12 staffs comprising of 7 females and 5 males.

Find the probability that the employer gives vacation hours to 3 males and 3 females if she chooses 6 students from the class at random.

Answer: the required probability is 0.3788

Step-by-step explanation:

Given that;

Total number of staffs = 12

7 females and 5 males

now

Total number of ways to 6 staffs from 12  = ¹²C₆

Number of ways of selecting 3 females and 3 males = ⁷C₃ × ⁵C₃

so,

Probability that the employer gives vacation hours to 3 males and 3 females if she chooses 6 students from the class at random will be;

= ⁷C₃ × ⁵C₃ / ¹²C₆

= ( [7!/(3!×(7-3)!] × [5!/(3!×(5-3)!] ) / [12!/(6!×(12-6)!]

= [35 × 10] / 924

= 350 / 924

= 0.3788

Therefore, the required probability is 0.3788