# statistics and probability 26

Five-card stud is a poker game, in which a player is dealt 5 cards from an ordinary deck of 52 playing cards. How many distinct poker hands could be dealt?

How many different ways can you arrange the letters X, Y, and Z without repeating letters? (Hint: In this problem, order is important; i.e., XYZ is considered a different arrangement than YZY.)

In horse racing, a trifecta is a type of bet. To win a trifecta bet, you need to specify the horses that finish in the top three spots in the exact order in which they finish. If eight horses enter the race, how many different ways can they finish in the top three spots?

How many sample points are in the sample space when a coin is flipped 4 times and each time the result (heads or tails) is recorded?

A business man has 4 dress shirts and 7 ties. How many different shirt/tie outfits can he create?

Joleen is on a shopping spree. She buys six tops, three shorts and 4 pairs of sandals. How many different outfits consisting of a top, shorts and sandals can she create from her new purchases?

What is the total number of possible 4-letter arrangements of the letters
m, a, t, h, if each letter is used only once in each arrangement?

There are 12 boys and 14 girls in Mrs. Schultzkie’s math class. Find the number of ways Mrs. Schultzkie can select a team of 3 students from the class to work on a group project. The team is to consist of 1 girl and 2 boys.

The ski club with ten members is to choose three officers captain, co-captain & secretary, how many
ways can those offices be filled?

For a segment of a radio show, a disc jockey (Dr. Jams) can play 4 songs. If there are 8 to select from, in how many ways can the program for this segment be arranged?

A combination lock can be set to open to any 3-letter sequence. How many such sequences are possible?

A teacher has 5 different books to be arranged side by side. How many different arrangements are possible?

From a group of 8 professors, a committee is selected to develop a new curriculum. How many committees can be formed with five numbers of members?

Three managers are to be selected from a group of 30 to work on a project. In how many different ways can the managers be selected?

The managers are to be selected from a group of 30 to work on a project. In how many different ways can the group of 3 be selected if a certain manager must work on the project?

The managers are to be selected from a group of 30 to work on a project. In how many different ways can a nonempty group of at most 3 managers be selected from these 30 managers?

Morse code uses sequence of dots and dashes to represent letters and words. How many sequences are possible with at most 3 symbols?

A television talk show will include 4 women and 3 men as panelists. In how many ways can the panelists be seated in a row of 7 chairs?

A television talk show will include 4 women and 3 men as panelists. In how many ways can the panelists be seated in a row of 7 chairs if the men and women are to be alternated?

A television talk show will include 4 women and 3 men as panelists. In how many ways can the panelists be seated in a row of 7 if the men must sit together and the women must sit together?

In how many ways can a full house of aces and eights (3 aces and 2 eights) be dealt in a 5-card poker hand?

Five cards are dealt from a standard 52-card deck. How many such hands have exactly 2 hearts?

Five cards are dealt from a standard 52-card deck. How many such hands have all cards of a single suit?