91Ó°ÊÓ

Suppose that six distinct integers are selected from the set \(\\{1,2,3,4,5,6,7,8,9,10\\} .\) Prove that at least two of the six have a sum equal to 11. Hint: Consider the partition {1,10} , {2,9},{3,8},{4,7},{5,6}.

Determine the number of strings that can be formed by ordering the letters given. SUGGESTS

Use the Multiplication Principle. The options available on a particular model of a car are five interior colors, six exterior colors, two types of seats, three types of engines, and three types of radios. How many different possibilities are available to the consumer?

In how many ways can we select a chairperson, vice chairperson, and recorder from a group of 11 persons?

How many strings can be formed by ordering the letters SALESPERSONS if no two \(S\) 's are consecutive?

Use the Multiplication Principle. A restaurant chain advertised a special in which a customer could choose one of five appetizers, one of 14 main dishes, and one of three desserts. The ad said that there were 210 possible dinners. Was the ad correct? Explain.

Professor Euclid is paid every other week on Friday. Show that in some month she is paid three times.

In how many different ways can 12 horses finish in the order Win, Place, Show?

How many strings can be formed by ordering the letters SCHOOL using some or all of the letters?

Is it possible to interconnect five processors so that exactly two processors are directly connected to an identical number of processors? Explain.