Q63.This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . (1) Statement −1 is true, Statement −2 is true; (2) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1 (3) Statement −1 is false, Statement- 2 is true. (4) Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement −1
What This Question Tests
This question tests the understanding of the stars and bars method for distributing identical items into distinct boxes (Statement-1) and the fundamental definition of combinations (Statement-2). Both statements are true, and Statement-2 provides the combinatorial basis for the formula used in Statement-1.
Concepts Tested
Formulas Used
C(n, r) = n! / (r! * (n-r)!)
Number of ways to distribute n identical items into r distinct boxes such that no box is empty = C(n-1, r-1)
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📋 Question Details
- Chapter
- Permutation & Combination
- Topic
- Distribution of identical items, Combinations
- Year
- 2011
- Shift
- Unknown
- Q Number
- Q63
- Type
- Assertion Reasoning
- NCERT Ref
- Class 11 Mathematics Ch 7: Permutation and Combination
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