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Twelve students are in a campus organization. Eight of the students are juniors, and four are...

Twelve students are in a campus organization. Eight of the students are juniors, and four are seniors. They need to pick a group of five students to represent their organization at freshman orientation. How many different ways can they pick this group, if at least two of the students must be juniors?

Math   Statistics-And-Probability   
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Answer #1

12 students

8 are juniors

4 are seniors

5 students to pick up randomly

number of ways these 5 students are picked in such ways that atlest two or the student are junior = ?

n(atleast 2 are junior) = n(total) - n(less than 2 are junior)

n(atleast 2 are junior) = n(total) - n(no juniors) - n(1 junior)

we can not pick 5 students with no juniors so n(no juniors) = 0

n(atleast 2 are junior) =

n(atleast 2 are junior) =

n(atleast 2 are junior) =11*9*8 - 8

n(atleast 2 are junior) =792-8 = 784

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