📐 Mathematics · Permutations and Combinations · JEE

The number of ways to distribute n identical objects into r distinct groups (some may be empty):

Answer: C(n+r-1, r-1).

A n!/(r!)
B C(n+r-1, r-1)
C C(n,r)
D r<sup>n</sup>

Correct answer: B. C(n+r-1, r-1)

Explanation: Stars and bars: place n stars and r−1 bars. Total positions = n+r−1, choose r−1 for bars. Formula: C(n+r−1, r−1). Allows empty groups.

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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The number of ways to distribute n identical objects into r distinct groups (some may be empty):

Concept context

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