Consider three boxes, each containing 10 balls labelled 1 ,   2 ,   … . ,   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 t h box, i = 1 ,   2 ,   3 . Then, the number of ways in which the balls…

Question

Consider three boxes, each containing 10 balls labelled 1 , &#160; 2 , &#160; &#8230; . , &#160; 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 t h box, i = 1 , &#160; 2 , &#160; 3 . Then, the number of ways in which the balls can be chosen such that n 1 &#60; n 2 &#60; n 3 is :

Aicharya · Accepted Answer

Each box contains 10 balls numbered from 1 to 10 . n 1 , &#8201; n 2 , &#8201; n 3 are numbers on the balls drawn from the box B 1 , &#8201; B 2 and B 3 respectively such that n 1 &#60; n 2 &#60; n 3 . i.e., all 3 numbers n 1 , &#8201; n 2 , &#8201; n 3 must be different and can be arranged only in one way (increasing). Now n 1 , &#8201; n 2 , &#8201; n 3 can be selected in 10 C 3 ways. Hence, total number of ways = 10 C 3 . 1 = 10 C 3 = 10 ! 3 ! 7 ! = 10 &#215; 9 &#215; 8 3 &#215; 2 = 120 .

Consider three boxes, each containing 10 balls labelled 1 ,   2 ,   … . ,   10 .…

Solution

Consider three boxes, each containing 10 balls labelled 1 , &#160; 2 , &#160; &#8230; . , &#160; 10 .…

Solution

Consider three boxes, each containing 10 balls labelled 1 , 2 , … . , 10 .…