There are 17 appetizers available at a restaurant. From these, Charmaine is to choose 13 for her party. How many groups of 13 appetizers are possible?
Question
There are 17 appetizers available at a restaurant. From these, Charmaine is to choose 13 for her party. How many groups of 13 appetizers are possible?
Solution
The problem can be solved using the concept of combinations in mathematics. In combinations, the order of selection does not matter.
The formula for combinations is:
C(n, r) = n! / [(n-r)! * r!]
where:
- n is the total number of options,
- r is the number of options to choose,
- "!" denotes factorial, which is the product of all positive integers up to that number.
In this case, n = 17 (the total number of appetizers) and r = 13 (the number of appetizers Charmaine wants to choose).
So, the number of ways Charmaine can choose 13 appetizers from 17 is:
C(17, 13) = 17! / [(17-13)! * 13!]
Calculating the factorials:
17! = 17 * 16 * 15 * 14 * 13! (17-13)! = 4! = 4 * 3 * 2 * 1 13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Substituting these values into the formula:
C(17, 13) = (17 * 16 * 15 * 14 * 13!) / (4 * 3 * 2 * 1 * 13!)
The 13! in the numerator and denominator cancel out:
C(17, 13) = (17 * 16 * 15 * 14) / (4 * 3 * 2 * 1)
Calculating the result:
C(17, 13) = 2380
So, there are 2380 different groups of 13 appetizers that Charmaine can choose from the 17 available.
Similar Questions
How many groups of 13 appetizers are possible?
Answer the questions below.(If necessary, consult a list of formulas.)(a) There are 16 appetizers available at a restaurant. From these, Abdul is to choose 12 for his party. How many groups of 12 appetizers are possible?(b) A certain committee consists of 16 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 office
A new restaurant is promoting its place by giving every guest a choice of one piece out of 5 appetizers, 5 meat main courses, 5 seafood main courses, 5 desserts, and 20 drinks. How many combinations are possible for each guest?
A restaurant offers a dinner special where a customer can get an appetizer, an entrée, and a dessert all for one price. How many different dinner specials are possible if there are a choice of 6 appetizers, 12 entrees, and 8 desserts?
Isabel is arranging 11 cans of food in a row on a shelf. She has 7 cans of carrots, 3 cans of beans, and 1 can of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.