# This Week’s Math Problem: The Answer to the One About Being a Player

February 5, 2010

Every Monday, I’ll be posting a math problem on this site; every Friday, I’ll post the answer to that week’s problem. Here is Monday’s problem again — click “Read More” for the explanation, and then come back Monday for a new quantitative challenge!

**This Week’s Math Problem: **

You are a player who intends to schedule one date every day of the week, plus an extra on Saturday. If you have already made plans for Sunday through Wednesday, and have an additional 10 people on a waiting list to go out with you, how many different social schedules could you arrange for the week?

**The Answer: 5,040**

If you’ve already made plans for Sunday through Wednesday, then you have four date-slots left to fill: Thursday, Friday, Saturday afternoon, and Saturday evening. Since you have 10 choices available and “order matters” (that is, going out with A on Thursday, B on Friday, and C and then D on Saturday is a different social schedule then going out with A, B, C, and D in a different order), we simply multiply 10 x 9 x 8 x 7 to get the answer, 5,040.

For those who haven’t seen a problem like this before, the logic is: you have 10 choices for the first date. But once you’ve chosen someone, you have only 9 options left for the second date, etc. And, of course, the Fundamental Counting Principle tells us that we multiply to get the final answer.

Note: A plethora of people got this in the comments! Accordingly, next week’s problem will be harder! See you Monday!

#### Comments

**3 Responses to “This Week’s Math Problem: The Answer to the One About Being a Player”**

**Got something to say?**

A plethora of people got this in the comments!I don’t know. I would have called it more of a gaggle.

By the way, it occurred to me that you didn’t specify that each date had to be with a different person. If you are allowed to date the same person more than once, it’d just be 10×10x10×10=10,000. (It’s interesting that that the possibilities almost double. Well, it’s interesting to me at least.)

[...] Before I get into this, though, I’d like to say that next week’s math problem will be MUCH easier, for several reasons. One is that my purpose in posting math problems in the first place was more to interest those of general nerdy inclinations in humorous situations that could be made more sense of through math. However, it also sort of seemed natural for me to escalate the problems as the weeks went by, just because, since the Enlightenment, we pretty much just like to push things forward for their own sake (thanks, Voltaire!) So, I think I shall resist that impulse in the future. For instance, I was pretty happy with The One About Being a Player. [...]