First slide

Combinations

Question

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 $^{9} C_{3}$ .

Moderate

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

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.

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