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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 9C3.
Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3.
- 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 false.
- Statement-1 is false, Statement-2 is true.
- Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Correct answer: Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Solution
Statement-1 is correct because distributing 10 identical balls into 4 distinct boxes with no empty boxes can be visualized as placing dividers among the balls, which leads to the combinatorial expression 9C3. Statement-2 is also correct as it accurately describes the number of ways to choose 3 places from 9, and it serves as a valid explanation for the distribution method used in Statement-1.
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