#### Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is Statement-2 : The number of ways of choosing any 3 places from 9 different places is Option 1) Statement-1 is true, Statement-2 is false. Option 2) Statement-1 is false, Statement-2 is true. Option 3) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Option 4) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

As we learnt in

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

- wherein

Where

Let 4 distinct boxes be x, y, z and w

x + y + z + w = 10,

x' + y' + z' = 6

ways =

Correct option is 3.

Option 1)

Statement-1 is true, Statement-2 is false.

This is an incorrect option.

Option 2)

Statement-1 is false, Statement-2 is true.

This is an incorrect option.

Option 3)

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

This is the correct option.

Option 4)

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

This is an incorrect option.