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  • Confused! kindly explain, - Consider three boxes, each containing 10 balls labelledSuppose one ball is randomly drawn from eac - Permutations and combinations - JEE Main

Consider three boxes, each containing 10 balls labelled 1,2,\cdots ,10. Suppose one ball is randomly drawn from each of the boxes. Denote by n_{i}, the label of the ball drawn from the i^{th} box, \left ( i=1,2,3 \right ). Then, the number of ways in which the balls can be chosen such that n_{1}< n_{2}< n_{3} is : 

  • Option 1)

     

    164

  • Option 2)

     

    120

  • Option 3)

     

    82

  • Option 4)

     

    240

Answers (1)

best_answer

 

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

 

^{10}C_3 = \frac{10!}{3!\;7!} = \frac{10\times 9\times 8}{6\times 2} = 120 \;\textup{ways}


Option 1)

 

164

Option 2)

 

120

Option 3)

 

82

Option 4)

 

240

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