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A few possibilities off the top of my head:

  • Students and chairs. How many ways are there for $n$ students to sit in $k$ chairs. The game of musical chairs might be fun to play around with. One can also consider natural restrictions, such as myopic students who need to sit near the front.
  • Replace "men" and "women" with faculty from different departments. For example, you might need a curriculum committee made up of mathematicians and physicists.
  • In the senate, there are two senators from each state. How many ways are there of making a committee of 6 senators, no two of which are from the same state? This really only works in the US, but I am sure that there are similar phrasings that could work elsewhere. One could also consider party affiliation here, which could lead to more interesting problems.
  • True story: My daughter, who is in kindergarten, has a 5th grade "reading buddy." If there are $n$ kindergarteners and $k$ 5th graders, how many ways are their of pairing up students? If you want to appeal to an older audience, maybe we are pairing up tutors with students for individual instruction?
  • This is totally not what you want, but still an interesting problem: how many injective functions exist from a set with $n$ elements to a set with $k$ elements? How about surjective functions? How does this change with $n$ and $k$?
  • This question on MSE uses 9th and 10th graders. "Juniors" and "Seniors" could easily replace these if you wanted a college aged example.

A few possibilities off the top of my head:

  • Students and chairs. How many ways are there for $n$ students to sit in $k$ chairs. The game of musical chairs might be fun to play around with. One can also consider natural restrictions, such as myopic students who need to sit near the front.
  • Replace "men" and "women" with faculty from different departments. For example, you might need a curriculum committee made up of mathematicians and physicists.
  • In the senate, there are two senators from each state. How many ways are there of making a committee of 6 senators, no two of which are from the same state? This really only works in the US, but I am sure that there are similar phrasings that could work elsewhere. One could also consider party affiliation here, which could lead to more interesting problems.
  • True story: My daughter, who is in kindergarten, has a 5th grade "reading buddy." If there are $n$ kindergarteners and $k$ 5th graders, how many ways are their of pairing up students? If you want to appeal to an older audience, maybe we are pairing up tutors with students for individual instruction?
  • This is totally not what you want, but still an interesting problem: how many injective functions exist from a set with $n$ elements to a set with $k$ elements? How about surjective functions? How does this change with $n$ and $k$?

A few possibilities off the top of my head:

  • Students and chairs. How many ways are there for $n$ students to sit in $k$ chairs. The game of musical chairs might be fun to play around with. One can also consider natural restrictions, such as myopic students who need to sit near the front.
  • Replace "men" and "women" with faculty from different departments. For example, you might need a curriculum committee made up of mathematicians and physicists.
  • In the senate, there are two senators from each state. How many ways are there of making a committee of 6 senators, no two of which are from the same state? This really only works in the US, but I am sure that there are similar phrasings that could work elsewhere. One could also consider party affiliation here, which could lead to more interesting problems.
  • True story: My daughter, who is in kindergarten, has a 5th grade "reading buddy." If there are $n$ kindergarteners and $k$ 5th graders, how many ways are their of pairing up students? If you want to appeal to an older audience, maybe we are pairing up tutors with students for individual instruction?
  • This is totally not what you want, but still an interesting problem: how many injective functions exist from a set with $n$ elements to a set with $k$ elements? How about surjective functions? How does this change with $n$ and $k$?
  • This question on MSE uses 9th and 10th graders. "Juniors" and "Seniors" could easily replace these if you wanted a college aged example.
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A few possibilities off the top of my head:

  • Students and chairs. How many ways are there for $n$ students to sit in $k$ chairs. The game of musical chairs might be fun to play around with. One can also consider natural restrictions, such as myopic students who need to sit near the front.
  • Replace "men" and "women" with faculty from different departments. For example, you might need a curriculum committee made up of mathematicians and physicists.
  • In the senate, there are two senators from each state. How many ways are there of making a committee of 6 senators, no two of which are from the same state? This really only works in the US, but I am sure that there are similar phrasings that could work elsewhere. One could also consider party affiliation here, which could lead to more interesting problems.
  • True story: My daughter, who is in kindergarten, has a 5th grade "reading buddy." If there are $n$ kindergarteners and $k$ 5th graders, how many ways are their of pairing up students? If you want to appeal to an older audience, maybe we are pairing up tutors with students for individual instruction?
  • This is totally not what you want, but still an interesting problem: how many injective functions exist from a set with $n$ elements to a set with $k$ elements? How about surjective functions? How does this change with $n$ and $k$?