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

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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 ${ }^{9} C _{3}$
Statement- 2 : The number of ways of choosing any 3 places from 9 different places is ${ }^{9} C _{3}$

AIEEEAIEEE 2011Permutations and Combinations

Solution:

Number of ways to distribute 10 identical balls in four distinct boxes such that no box remains empty $={ }^{10-1} C_{4-1}={ }^{9} C_{3}$
Number of ways to select 3 different places from 9 places $={ }^{9} C _{3}$
Clearly statement- 2 is not a correct explanation of statement-1