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8 CHILDREN PARTICIPATE IN A IN A CONTEST. FOUR DIFFERENT PRIZES ARE AWARDED T0 THE WINNER AND THE FIRST,SECOND AND THIRD RUNNER UPS. IN HOW MANY DIFFERENT WAYS CAN THE FOUR PRIZES BE AWARDED?

Respuesta :

We have that there are 8 participants and 4 prizes, in this problem, it's important the order of the prizes too.

Now, for the first time, there are 8 possibilities for awarding the winner prize.

For the second moment, there are just 7 possibilities for awarding the first runner-up.

Then, we have that there are 6 possibilities for awarding the second runner-up.

And, finally, we have 5 possibilities for awarding the third runner-up.

So, we have that all the ways are represented as:

[tex]8\ast7\ast6\ast5=1680[/tex]

And since the order of the 4 prizes is important to get a specific prize, we have:

[tex]\frac{1680}{4!}=70[/tex]

Then the correct answer would be 70.

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