3.2 宿題

9³ =

P(9,3) =

729

504

In how many ways can six people line up at a single counter to order food and drinks at Taco Bell?

Six people can line up in [ ] ways.

７２０

A three-letter code is created by choosing letters from the set {A, B, C, D, E, F, G, H, I, J}.

a. How many codes are possible if letters cannot be repeated?
[ ] ways

b. How many codes are possible if letters can be repeated?
[ ] ways

７２０

１０００

The History Department at a college consists of 26 professors. How many ways can the department select three professors to hold the positions of Chair, Assistant Chair, and Graduate Director?

[ ] ways

１５６００

Suppose 4 different contracts are distributed amongst 11 different firms.

a. How many different ways can the contracts be awarded if any one firm can be awarded multiple contracts?
[ ] ways

b. How many different ways can the contracts be awarded if any one firm cannot be awarded multiple contracts?
[ ] ways

１４６４１

７９２０

A group of three boys and three girls are seated in a row of six chairs in an auditorium.

a. How many ways can they be seated in the six chairs if they may sit in any order?
☐ ways

b. How many ways can they be seated in the six chairs if they must alternate gender (i.e., boy-girl-boy-girl-… or girl-boy-girl-boy-…)?
☐ ways

７２０

７２

A message is created by arranging three different colored flags vertically on a flagpole of a ship. If a ship has 10 flags to choose from, how many different signals are possible?

[ ] signals can be created.

７２０

A cross country team consists of six players and two coaches. How many ways can the eight individuals pose for a picture by standing in a single line if the two coaches must stand together (in any order) on one end of the line?

[ ] arrangements are possible

２８８０

Find the number of distinguishable permutations of the eight letters in the word LOLLYPOP.

[ ] distinguishable permutations of LOLLYPOP

１６８０

A 9-character password must satisfy the following conditions:

• 2 letters (case is not sensitive), chosen from the 26 letters of the alphabet

• 4 digits, chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

• 3 symbols, chosen from the set {#, @, $, %}

a. How many passwords can be created if the 9 characters are chosen without replacement?
[ ] ways

b. How many passwords can be created if the 9 characters are chosen with replacement?
[ ] ways

７８６２４０００

４３２６４００００

How many ways can all of the letters in the word MUSKRAT be arranged to form seven-letter words?
Each word formed may or may not be a real word in the English language.

[ ] ways

5040

A class consists of 10 students (five boys and five girls) and one teacher. How many ways can the STUDENTS sit in a circle?

[ ] ways

円なので（１０－１）！＝９！

３６２８８０

A game is played with a circular spinner that contains 7 different colors. The design of the spinner is the order in which the colors are arranged.

How many ways can this spinner be designed?

[ ] ways

円形スピナーなので（７－１）！＝６！

７２０