#20 ### Educational Resources on Combinatorics and Probability#### Problem 18**Question:** A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 5 types of drinks to choose from, 5 types of sandwiches, and 3 types of chips. How many different value meal packages are possible?**Answer:** 75*Explanation:* The number of different value meal combinations can be calculated by multiplying the number of choices for each component: \[ \text{Total packs} = 5 \, (\text{drinks}) \times 5 \, (\text{sandwiches}) \times 3 \, (\text{chips}) = 75 \]#### Problem 19**Question:** Evaluate the following expression: \( 12! \)**Answer:** 479,001,600*Explanation:* The notation \( 12! \) represents the factorial of 12, which is the product of all positive integers up to 12:\[ 12! = 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 479,001,600 \]#### Problem 20**Question:** Reginald wants to buy a new collar for each of his 3 dogs. The collars come in a choice of 7 different colors.**Step 1:** How many selections of collars for the 3 dogs are possible if repetitions of colors are allowed?**Answer:** ____*Explanation:* Assuming each dog can have any of the 7 different colors, and the same color can be used more than once, the number of possible combinations is: \[ 7 \, (\text{colors for Dog 1}) \times 7 \, (\text{colors for Dog 2}) \times 7 \, (\text{colors for Dog 3}) = 7^3 = 343 \]**Step 2:** How many selections of collars are possible if repetitions of colors are not allowed?**Answer:** ____*Explanation:* If each dog must have a different collar color, the number of possible selections can be calculated using permutations: \[ 7 \, (\text{choices for Dog 1}) \times 6 \, (\text{choices

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Description: #20 ### Educational Resources on Combinatorics and Probability#### Problem 18**Question:** A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 5 types of drinks to choose from, 5 types of sandwiches, and