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Question
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; 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.
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Solution
The correct option is D Statement-1 is true, Statement-2 true; Statement-2 is a correct explanation for Statement-1.
The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box empty is same as the number of ways of selecting (r-1) places out of (n-1) different places, that is n−1Cr−1
Different places, that is 10−1C4−1=9C3.
∴ Both statements are correct and second statement
is a correct explanation of statement-1.
The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box empty is same as the number of ways of selecting (r-1) places out of (n-1) different places, that is n−1Cr−1
Different places, that is 10−1C4−1=9C3.
∴ Both statements are correct and second statement
is a correct explanation of statement-1.
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