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Q.

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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a

Statement 1 is false, Statement 2 is true

b

Statement 1 is true, Statement 2, is true; Statement 2 is the correct explanation for Statement 1

c

Statement 1 is true; Statement 2 is true; Statement 2 is not as correct explanation for Statement 1

d

Statement 1 is true, Statement 2 is false

answer is C.

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Detailed Solution

Number of ways to distribute 10 identical balls in four distinct boxes such that no box remains empty=10−1C4−1=9C3Number of ways to select 3 different places from 9 places = 9C3.Clearly statement-2 is not a correct explanation of statement-1.
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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.