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In how many ways can 10 identical presents be distributed among 6 children so that each child gets at least one present?
- a)15C5
- b)16C6
- c)9C5
- d)610
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In how many ways can 10 identical presents be distributed among 6 chil...
We have to count natural numbers which have a maximum of 4 digits. The required answer will be given by: Number of single digit numbers + Number of two digit numbers + Number of three digit numbers + Number of four digit numbers.
Most Upvoted Answer
In how many ways can 10 identical presents be distributed among 6 chil...
The question says that each child must get at least one present.
So, let's start by giving one present to each child. Number of presents remaining = 10-6 = 4.
Now we need to count the ways to distribute 4 presents among 6 children.
We can use the formula = n+(r-1)C(r-1) where n = 4 and r = 6
that gives us: 4+(6-1)C(6-1)
= 9C5
You can refer to articles about the distribution of n identical objects among r participants to understand where the formula comes from.
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In how many ways can 10 identical presents be distributed among 6 chil...
Problem: In how many ways can 10 identical presents be distributed among 6 children so that each child gets at least one present?
Solution: We can solve this problem using the stars and bars method. Let's assume we have 10 stars representing the 10 presents and 5 bars representing the 6 children. The bars will be used to separate the presents for each child. For example, if we have the following arrangement:
**|****|***|****|*|****
It means that the first child gets 2 presents, the second child gets 4 presents, the third child gets 3 presents, the fourth child gets 1 present, and the fifth and sixth children get no presents.
To ensure that each child gets at least one present, we need to arrange the stars and bars in such a way that no two bars are adjacent. This is because if two bars are adjacent, it means that one child is not getting any present.
So, we need to choose 5 positions out of the 9 possible positions (5 bars and 10 stars) to place the bars. The number of ways to do this is given by the combination formula:
C(9,5) = 9! / (5! * 4!) = 126
Therefore, the number of ways to distribute the 10 presents among 6 children so that each child gets at least one present is 126, which is option (c).
Solution: We can solve this problem using the stars and bars method. Let's assume we have 10 stars representing the 10 presents and 5 bars representing the 6 children. The bars will be used to separate the presents for each child. For example, if we have the following arrangement:
**|****|***|****|*|****
It means that the first child gets 2 presents, the second child gets 4 presents, the third child gets 3 presents, the fourth child gets 1 present, and the fifth and sixth children get no presents.
To ensure that each child gets at least one present, we need to arrange the stars and bars in such a way that no two bars are adjacent. This is because if two bars are adjacent, it means that one child is not getting any present.
So, we need to choose 5 positions out of the 9 possible positions (5 bars and 10 stars) to place the bars. The number of ways to do this is given by the combination formula:
C(9,5) = 9! / (5! * 4!) = 126
Therefore, the number of ways to distribute the 10 presents among 6 children so that each child gets at least one present is 126, which is option (c).
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In how many ways can 10 identical presents be distributed among 6 children so that each child gets at least one present?a)15C5b)16C6c)9C5d)610Correct answer is option 'C'. Can you explain this answer?
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