Math Problems, Proportions Problems

Problem of the Day: 12/24/12

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:
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: \frac{1}{15504}.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s