Question

A game on The Price is Right has the contestant choose 12 tiles from a wall containing 25 tiles. Of the 25 ​tiles, 12 have a dollar sign on the back and the rest are blank. If all 12 of the tiles the constestant picks have a dollar​ sign, the contestant wins​ $100,000. However, if they pick just 10 tiles with the dollar​ sign, they win​ $10,000. In how many ways could the contestant pick exactly 10 of the 12 tiles with a dollar​ sign?

Answer 1

Here, we are given that,

A game on The Price is Right has the contestant choose 12 tiles from a wall containing 25 tiles. Of the 25 ​tiles, 12 have a dollar sign on the back and the rest are blank. If all 12 of the tiles the constestant picks have a dollar​ sign, the contestant wins​ $100,000. However, if they pick just 10 tiles with the dollar​ sign, they win​ $10,000.

From this given information, we have to answer the given question:-

In how many ways could the contestant pick exactly 10 of the 12 tiles with a dollar​ sign?

Here, total tiles =25

Dollar sign tiles = 12

i.e. Non Dollar sign tiles = (25-12)= 13

Now, we randomly select 12 tiles out of 25.

Total no. Of ways of selection = ( 25 C 12 )

= 5,200,300

Now, we have to obtain the number of ways that in a random sample of 12 , we get exactly 10 Dollar sign tiles.

That means, 10 are Dollar sign tiles and 2 are non Dollar sign tiles.

This can happen in ( 12 C 10 ) * (13 C 2 ) ways

= ( 12 C 10 ) * (13 C 2 )

= ( 66 ) * ( 78 )

= 5148

Hence, the contestant could pick exactly 10 of the 12 tiles with a dollar​ sign in 5148 ways.

This answers your question.

If you have understood the answer please rate Positively.