## Online Course Discussion Forum

### MC II-B HW Questions

On 3.14 you might want to use complementary counting. To find how many ways are there in total try doing something similar to what is done in the example question 3.2.

For 3.23, you could find, with stars and bars, the number of solutions to the equation $a+b+c = 10$ where each number is at least $0$. This time, however, you need to make sure each number is at least $2$. What would you need to do different so you can still use stars and bars?

For 30, you can think of the people in the elevator as identical balls and each of the floors where they can get out as boxes. So part (a) turns into "in how many ways can you place $5$ identical balls into $10$ different boxes?" And part (b) turns into "in how many different ways can you pick $5$ different boxes?"

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