Question:
The number of ways in which we can distribute n identical balls in k boxes is
The number of ways in which we can distribute n identical balls in k boxes is
Updated On: May 29, 2024
\((n+k-1)C_{k-1}\)
\((n)C_{k-1}\)
\((n-1)C_{k-1}\)
\((n+k-1)C_{k}\)
\(nC_{k}\)
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The Correct Option is A
Solution and Explanation
From the give data we can write,
The number of ways to distribute n identical balls into k distinct boxes is
The solution can be formed by using the concept of combination.(Note -Where only selection is important aspect.)
So, the number of ways to distribute n identical balls into k distinct boxes is
\((n+k-1)C_{k-1}\) (_Ans)
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.