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  • Answer please! - Permutations and combinations - JEE Main

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}.

 

  • 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.

 

Answers (1)

best_answer

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.

^{n}c_{r}=\frac{(n)!}{r!(n-r)!}

- wherein

Where 1\leq r\leq n

 

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

x + y + z + w = 10, 

x\geq1\ \; y\geq1

z\geq1\ \; w\geq1

x' + y' + z' = 6

ways = ^{9}C_{3}

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.

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