Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 93 .Statement-2 : The number of w - Mathematics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is (3 9) .Statement-2 : The number of ways of choosing any 3 places from 9 different places is (3 9) .

A $Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1$
B $Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1$
C $Statement-1 is false, Statement-2 is true.$
D $Statement-1 is true, Statement-2 is false.$

Solution & Step-by-step Explanation

Statement 1: Distributing n identical items into r distinct bins with at least 1 in each is (r - 1 n - 1) . Here (4 - 1 10 - 1) = (3 9) . Correct.Statement 2: The definition of combination (r n) is choosing r items/places from n . So (3 9) is choosing 3 from 9. Correct.The logic of the "stars and bars" formula for non-empty bins is exactly placing r - 1 dividers in n - 1 available gaps between items. This is a choice of 3 spots from 9. Thus Statement 2 explains Statement 1.

Try it yourself before checking the explanation above.

Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is (3 9) .Statement-2 : The number of ways of choosing any 3 places from 9 different places is (3 9) .

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Statement-1 is false, Statement-2 is true.

Statement-1 is true, Statement-2 is false.

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