4. Probability

Traveling Salesperson A salesperson must travel to eight cities to promote a new marketing campaign. How many different trips are possible if any route between cities is possible?

[NW] Selecting a Jury

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.

b. What is the probability of selecting a jury of all faculty?

Selecting a Committee

Suppose that there are 55 Democrats and 45 Republicans in the U.S. Senate. A committee of seven senators is to be formed by selecting members of the Senate randomly.

a. What is the probability that the committee is composed of all Democrats?"

Selecting a Committee

Suppose that there are 55 Democrats and 45 Republicans in the U.S. Senate. A committee of seven senators is to be formed by selecting members of the Senate randomly.

c. What is the probability that the committee is composed of three Democrats and four Republicans?

List all permutations of five objects a, b, c, d, and e taken three at a time without replacement.

Text Twist

In the game Text Twist, six letters are given and the player must form words of different lengths using those letters. Suppose the letters in a particular game are ENHSIC.

a. How many different arrangements are possible using all 6 letters?

In the game of Jumble, the letters of a word are scrambled. The player must form the correct word. In a recent game in a local newspaper, the Jumble “word” was LINCEY. How many different arrangements are there of the letters in this “word”?

A __________ is an ordered arrangement of r objects chosen from n distinct objects without repetition.

A __________ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order.

"Determine the value of each of the following:

b. 0!"