Combinatorics problem

Question

There are 3 parks to clean and the cleaning takes 2 days. How many different ways there are to schedule the cleaning, if it needs to be done during the first 5 days of the week.

Answer 1

Let's assume that it takes a total of 2 days to clean 3 parks, not 2 days to clean each park. If the latter were true it would take 3 x 2 or 6 days to do the job, but only 5 days are available.

So in 2 days 3 parks can be cleaned. So how many combinations (not permutations, since order doesn't count) of 2 days are there out of 5 days? (You'd get the same result if 4 or x number of parks could be done in a span of 2 days in total.)

5C2 = 10. You can use a scientific calculator or the formula nCr = n!/(n - r)!r!. You can also list the combinations: MT;MW;MTh:MF. Then TW;TTh;TF. Also WTh;WF and finally ThF.