Question

2. (For this problem, leave your answers in Combinatorics format – do NOT simplify). A conference is being held that faculty members from the IST department have been invited. There are 23 female and 19 male faculty members. Six members are randomly selected. What is the probability that

Answer 1

Answer:

Follows are the solution to this question:

Step-by-step explanation:

please find the complete question in the attached file.

female = 23  and male = 19 faculty members

Randomly selected member are = 6

In point 1:

The Probability to equally selecting men and women:

$= \frac{(23C3+19C3)}{42C6}$

In point 2:

The Probability of selecting at least 4 men:

$= \frac{((19C4 \times 23C2)+(19C5 \times 23C1)+(19C6))}{42C6}$

In point 3:

The probability in which no women are chosen implies that 6 selected members are from 23 women:

$= \frac{23C6 }{42C6}$

In point 4:

The Probability in which no more than 4 women are selected:

$\frac{((19C6)+(23C1 \times 19C5)+(23C2 \times 19C4)+(23C3 \times 19C3)+(23C4 \times 19C2))}{42C6}$