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

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 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 a correct explanation for Statement-1 (D) Statement- 1 is true, Statement- 2 is false

Tardigrade Admin · Accepted Answer

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

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​

Statement- 1 is false, Statement- 2 is true

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

Statement-1 is true, Statement-2 is true; Statement- 2 is not a correct explanation for Statement-1

Statement- 1 is true, Statement- 2 is false

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

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 $^{9} C_{3}$

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