# Could someone please tell me what this notation means?

vr0nvr0n

## Homework Statement

Erica goes swimming three out of the seven days of the week. How many possibilities are there for her swim schedule if she goes swimming on Monday or Tuesday or both? (Define M to be the set of schedules in which Erica goes swimming on Monday. Let T be the set of schedules in which Erica goes swimming on Tuesday.)

## Homework Equations

There are none. This section is merely on the inclusion-exclusion principle

## The Attempt at a Solution

I worked it out like this: Set of all possibilities for her schedule including Monday = Monday*6 choices*5 choices (because of the other days of the week) = 30. Same for Tuesday. In most problems, you would add the 30 and the 30 to make 60, but that doesn't make sense here since we are talking about a linear week.

If she went on both Monday and Tuesday, there would only be 5 possibilities for her schedule. Since those 5 possibilities overlap in both sets, subtract five from thirty to get the correct answer of 25 possibilities.

Anyways, for the program I'm using, when you get the answer correct a prompt pops up explaining the answer (which always seemed odd to me, and I have never paid much attention to it until today). The prompt that showed up explained it like this:

(for some reason, I am having difficulty embedding, so here is the link) https://imgur.com/TiuHWHV

So, my question is the notation showing the 6 and 2 in parentheses, I have never seen before. Obviously, there is a method for working out a problem like this mathematically instead of just logically, but I have scoured my textbook and have never come across this notation. What does this mean?

vr0n

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That notation refers to the binomial coefficient. It is often read "6 choose 2" or "6 things taken 2 at a time". It is a combinational quantity of the number of ways you can choose 2 items out of a group of 6.

vr0nvr0n
Thank you.

In case anyone else finds this in the future, that notation is mathematically equivalent to this formula:
If it is written as the example provided with (with 6 on top of 2), it is 6!/(2!(6-2)!) or 6!/(2!*4!).

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