# For each event, circle the most appropriate term. in a sweepstakes with nine hundred entries, the first winner selected receives the grand prize, the second receives first prize, and so on until...

For each event, circle the most appropriate term.

in a sweepstakes with nine hundred entries, the first winner selected receives the grand prize, the second receives first prize, and so on until all thirty prizes are awarded. How many possible outcomes are there?

counting principle. Combination. factoral. Permutation.

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### 2 Answers

In the sweepstakes with nine hundred entries, the first winner selected receives the grand prize, the second receives first prize, and so on until all thirty prizes are awarded. If the winners are chosen starting with the grand prize winner and moving on to winner number 30, the number of options for the first place is equal to 900, the number of options for the second place is 899 and so on. The order is relevant here because it makes a difference whether a person chosen as a winner wins the grand prize or prize number 30.

**This gives the total number of outcomes as P(900, 30) = `(900!)/((900-30)!)` = 900*899*898*...871**

The problem is to set 9 hundred entries in 30 awards palces.

So it's a combination:

`N= [[900,],[30,]]` `=(900!)/((900-30)!30!)=(900!)/(870!30!)=`

`=(871X872X873.....X900)/(30!)=` `=30X871X872X873....X899`

So there are

`8,6678871237690369055396476560318...10^86`

possible combinations.