In this work you are going to be focus on:Factorials and the Rule of Sum

Part A

For each question you are asked to:

a) identify the information given in the question.

b) determine the appropriate formula.

c) substitute the values given into the formula and find the solution.

My Questions are:

1.How many permutations are there of 7 people taken from 11 people?

2.If 10 different books are to be arranged on a shelf, in how many different ways can this be done?

3.Depending on the situation, a game allows a player to roll 1, 2, or 3 dice. How many possible outcomes are there?

4.How many ways are there to arrange either 4 or 5 toys from a basket of 12 toys?

5.A box contains 3 red, 5 green, 1 blue, 6 orange, and 4 black blocks. In how many ways could a child reach in and select a block?

6.Four players each are dealt one card. In how many ways could the cards all be clubs or honour cards (10, J, Q, K, A)?

7.Express in the form .

a)

b) 9!

c) 27 26 25

8.A club has 20 members. In how many ways could an executive committee consisting of a president, vice president, secretary, membership director, and treasurer be named? Show two methods.

9.A spinner has 6 sections, numbered from 1 to 6. The spinner is spun 4 times. How many different outcomes are possible?

10.) A combination lock uses the numbers from 1 to 60. How many unique three-number lock combinations are possible if repetition is permitted?

11. Fraternities and sororities often use the Greek alphabet to name their group. The Greek alphabet has 24 letters. If repetition is permitted, how many different fraternities or sororities could be named

a) using two letters?

b) using three letters?

12.From a graduating class of 175 students, the four students with the highest average marks will win academic awards. In how many ways could these awards be presented?

13.Using words and/or diagrams, explain why the number of arrangements of the letters ABCDE is 5!

14.How many ways are there to roll a sum divisible by three on two dice?

15.Determine the number of ways of arranging 4 or 5 books on a shelf from a box containing 12 books.