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For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations. How many ways are there to construct a string of 3 digits if numbers can be repeated?

For the following exercises, find the number of subsets in each given set. A set containing 5 distinct numbers, 4 distinct letters, and 3 distinct symbols

For the following exercises, find the distinct number of arrangements. The letters in the word 鈥渁cademia鈥� that begin and end in 鈥渁鈥�

For the following exercises, find the distinct number of arrangements. How many arrangements can be made from the letters of the word 鈥渕ountains鈥� if all the vowels must form a string?

A motorcycle shop has 10 choppers, 6 bobbers, and 5 caf茅 racers鈥攄ifferent types of vintage motorcycles. How many ways can the shop choose 3 choppers, 5 bobbers, and 2 caf茅 racers for a weekend showcase?

Susan bought 20 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 6 roses, and 8 daisies?

For the following exercises, use the Binomial Theorem to write the first three terms of each binomial. $$(3 a+b)^{20}$$

For the following exercises, four coins are tossed. Find the probability of tossing exactly three heads.

Use the following scenario for the exercises that follow: In the game of Keno, a player statts by selecting 20 numbers from the numbers 1 to \(80 .\) After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to \(80 .\) A win occurs if the player has correctly selected \(3,4,\) or 5 of the 20 winning numbers. (Round all answers to the nearest hundredth of a percent.) What is the percent chance that a player selects exactly 4 winning numbers?

What are the first five terms of the geometric sequence \(a_{1}=3, a_{n}=4 \cdot a_{n-1} ?\)