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

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:

In point 2:

The Probability of selecting at least 4 men:

In point 3:

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

In point 4:

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

1/5

step-by-step explanation:

the dice has 6 sides and there is only one 5 in a dice.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.