My class consists of 8 men and 7 women. I want to pick a group of 6 people for research. Write each answer using fraction as needed.
a. In how many different ways can I pick this group?
b. What is the probability of having exactly 3 men in the group?
c. What is the probability of all the selected people in group are women?
d. What is the probability of having at least one man in the group?

a.5005

b.

c.1/715

d.714/715

Step-by-step explanation:

We are given that

Total men=8

Total women=7

Total people, n=8+7=15

r=6

a.

Combination formula:

Selection of r out of n people by total number of ways

Using the formula

We have n=15

r=6

Total number of ways=

Total number of ways=

Using the formula

Total number of ways=

Total number of ways=5005

b. The probability of having exactly 3 men in the group

=

Using the formula

Probability,

The probability of having exactly 3 men in the group=

=

=

The probability of having exactly 3 men in the group

=

c. The probability of all the selected people in the group are women

=

The probability of all the selected people in the group are women

The probability of all the selected people in the group are women

d. The probability of having at least one man in the group

=1- probability of all the selected people in group are women

The probability of having at least one man in the group

The probability of having at least one man in the group

answer: do we write it

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.