Counting Rules and Probability

In how many ways can you answer six multiple choice questions if each question has four options?

• 4096

• 360

• 15

• 24

The University of Illinois has about 40,000 students. What is the minimum number of students needed to be certain that at least two students have the same 3 initials?

• 27

• 17,576

• 17,577

• 18,253

Twelve people toast each other at Thanksgiving dinner. If each person clinks a glass with every other person exactly once, how many clinks are there?

• 66

• 132

• 11

• .384

How many 4 digit numbers contain no 5's? The leading digit cannot be zero.

• 3,168

• 6,832

• 24

• 5,832

How many different "words" can be formed using all the letters of the word IMPARTIALITY?

• 479,001,600

• 19,958,400

• 79,833,600

• 39,916,800

How many permutations are possible if six people are seated around a square table?

• 720

• 30

• 120

• 6

Four couples go to the school's drama production and sit together in a row of 8 seats. In how many ways can these people arrange themselves if each couple sits together?

• 24

• 384

• 16

• 256

Seventy-five people buy a raffle ticket for a cake drawing with four cakes. If four tickets are to be drawn, how many ways are there to award the cakes if the four cakes are identical?

• 1,215,450

• 29,170,800

• 300

• 31,640,625

There are seven seats in each row of a classroom. Luke and Lester are assigned to after-school detention and they must sit in the front row of the classroom, but they cannot sit next to each other because they might talk. How many ways can these two students be seated in the row?

• 14

• 49

• 30

• 128

The City Council is made up of nine representatives and one Chairman. If a committee of four is formed from the members, find the probability that the committee includes the Chairperson.

• 0.4

• 0.12

• 2.5

• 0