## Description

**Question 5 which is a two part question, and question 8 needs work shown. Only one them two. The others do not need it.**

1. List all the ways to select two members from S with repetition. The order in which the members are selected is not important. For example, DD is allowed and BA is the same selection as AB. ** S={H,J,K,L,****M}** Identify the list of all the ways to select two members from S, allowing for repetition.

2. Assume you are rolling two dice; the first one is red, and the second is green. Use a systematic listing to determine the number of ways you can roll a total less than 7 on the two dice. In how many ways can you roll less than 7?

3. A designer has designed different tops, pants, and jackets to create outfits. How many different outfits can the models wear if she has designed the following pieces? **Three tops, five pants, two jackets ** There is a total of how many different outfits?

4. An equestrian club has eight members. If the club wants to select a president, vice president, and treasurer (all of whom must be different), in how many ways can this be done? How many ways can the three positions be filled?

5. Two Part Question / **Work needs shown for both sections for this question**.

(a) In a certain state, license plates have four letters followed by two digits. How many such license plates are possible?

(b) If the state department of transportation decides to change the plates to have two letters followed by four digits, how many plates will now be possible?

6. Simplify **5!** (Using an integer or a fraction)

7. Evaluate the expression **P(6,2) **

8. Evaluate the expression **C(10,6) Work needs show for this question**

9. Specify the number of ways to perform the task described. Give your answers using P(n, r) or C(n, r) notation. The key in recognizing whether a problem involves permutations or combinations is deciding whether order is important.

A hot sauce bar has 12 varieties. You are going to select 7 to taste, but you do not care about the order in which you taste them. How many number of ways can this task be performed?

## Explanation & Answer

Please find attached the answer in doc and PDF format. Please note both files are exactly same content-wise. Please let me know if you have any doubt.

1. List all the ways to select two members from S with repetition. The order in which the members

are selected is not important. For example, DD is allowed and BA is the same selection as

AB. S={H,J,K,L,M} Identify the list of all the ways to select two members from S,allowing for

repetition.

Answer:

𝒂. ℎℎ, ℎ𝑗, ℎ𝑘, ℎ𝑙, ℎ𝑚, 𝑗ℎ, 𝑗𝑗, 𝑗𝑘, 𝑗𝑙, 𝑗𝑚, 𝑘ℎ, 𝑘𝑗, 𝑘𝑘, 𝑘𝑙, 𝑘𝑚, 𝑙ℎ, 𝑙𝑗, 𝑙𝑘, 𝑙𝑙, 𝑙𝑚

2. Assume you are rolling two dice; the first one is red, and the second is green. Use a

systematic listing to determine the number of ways you can roll a total less than 7 on the two dice. In

how many ways can you roll less than 7?

Answer: 15

3. A designer has designed different tops, pants, and jackets to create outfits. How many different

outfits can the models wear if she has designed the following pieces? Three tops, five pants, two

jackets There is a total of how many different outfits?

Answer: 30

4. An equestrian club has eight members. If the club wants to select a president, vice president, and

treasurer (all of whom must be different), in how many ways can this be done? How many wa...