Santa’s elves are busy making Christmas gifts at the North Pole! They have to make 3 billion gifts in time for midnight on Christmas Eve – but luckily, they have 200,000 elves working at any given time. If each elf can make a gift in one minute (they’re highly trained), then on what day in December would the elves have to start making gifts?

*Solution to yesterday’s problem:*

To find the probability that five specific students are chosen out of 20, but the order of the students doesn’t matter, we can use combinations.

The number of possible ways that a group of five can be picked out of 20 is

To simplify this easily, we can rewrite the factorials as multiplications, then cancel:

Canceling,

Now we can do another round of dividing by common factors, like 20 and 5, 16 and 4 and 2, etc.

So the chance that these 5 particular students are chosen is incredibly small: .

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