91Ó°ÊÓ

A combination lock displays 50 numbers. To open it, you turn clockwise to the first number of the "combination," then rotate counterclockwise to the second number, and then rotate clockwise to the third number. (a) How many different lock combinations are there? (b) Comment on the description of such a lock as a combination lock.

Explain the difference between a permutation and a combination. Give an example to illustrate your explanation.

In a certain Algebra and Trigonometry class, there are 18 freshmen and 15 sophomores. Of the 18 freshmen, 10 are male, and of the 15 sophomores, 8 are male. Find the probability that a randomly selected student is: (a) A freshman or female (b) A sophomore or male

The faculty of the mathematics department at Joliet Junior College is composed of 4 females and 9 males Of the 4 females, 2 are under age \(40,\) and of the 9 males, 3 are under age \(40 .\) Find the probability that a randomly selected faculty member is: (a) Female or under age 40 (b) Male or over age 40

What is the probability that at least 2 people in a group of 12 people have the same birthday? Assume that there are 365 days in a year.

What is the probability that at least 2 people in a group of 35 people have the same birthday? Assume that there are 365 days in a year.

Lotto America is a multistate lottery in which 5 red balls from a drum with 52 balls and 1 star ball from a drum with 10 balls are selected. For a $$\$ 1$$ ticket, players get one chance at winning the grand prize by matching all 6 numbers. What is the probability of selecting the winning numbers on a $$\$ 1$$ play?

Simplify: \(\sqrt{108}-\sqrt{147}+\sqrt{363}\)