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 ${}^9{C}_3$

• A. Statement - 1 , Statement -2 both are true But Statement 2 is not a correct explanation for Statement 1
• B. Statement -1 is true, Statement - 2 is false.
• C. Statement -1 is false, Statement -2 is true
• D. Statement -1 is true, Statement - 2 is true, Statement - 2 is a correct explanation for Statement - 1

Answer 1

The correct option is A Statement - 1 , Statement -2 both are true But Statement 2 is not a correct explanation for Statement 1

Correct option (a)

Let the number of ways of distributing n identical objects among r persons such that each person gets at least one object in same as the number of ways of selecting $(r-1)$ places out of $(n-1)$ different places, i.e., ${}^{n-1}{C}_{r-1}$

Here, $n=10$,

$r=4$,

Statement I$={}^{10-1}{C}_{4-1}={}^9{C}_3$

Statement II$={}^9{C}_3$.