- 11/18/2022
- Mathematics
- High School
alice has 24 apples. in how many ways can she share them with becky and chris so that each of the people has at least 2 apples?
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Assuming Alice has 2 apples, there are 19 ways to split the rest of the apples with Becky and Chris.
The total number of ways to split 24 apples between the three friends is equal to 19 + 18 + 17 + 16 + 15 + ...……+ 2 + 1 = 20 x ( 19 / 2 ) = 190
Alice can share them with Becky and Chris in a variety of ways, as long as each person has at least 2 apples. For example, Alice could give Becky 8 apples and Chris 16 apples, or she could give Becky 10 apples and Chris 14 apples. As long as each person has at least 2 apples, there are many ways for Alice to share her apples.To split the apples, we employ the Ball-and-urn method, also referred to as "Sticks and Stones" or "Stars and Bars."
Hence there are 19 different ways she can share them with becky and chris so that each of the people has at least 2 apples.
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Answer
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Final answer:
There are 1330 ways to distribute 18 apples among three people ensuring each person has at least 2 apples.
Explanation:
To solve this problem, we can use the concept of combinations. Each person needs to have at least 2 apples, so we need to distribute the remaining 24-2-2-2 = 18 apples among three people. We can do this by using stars and bars, which means dividing the apples using dividers. In this case, we have three dividers and 18 stars (representing 18 apples). So, there are C(18+3, 3) = C(21, 3) = 1330 ways to distribute the remaining 18 apples among Alice, Becky, and Chris while ensuring each person has at least 2 apples.
Here's an example of how the distribution can be done: Let's represent an apple using '*'. So, we have 18 '*'. We can distribute them as '****|******|****', which means Alice has 4 apples, Becky has 7 apples, and Chris has 4 apples.
Learn more about Combinations here:
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