Final answer:
There are 126 ways to distribute 16 identical apples to 6 mathematics lecturers, with each lecturer receiving at least 2 apples.
Step-by-step explanation:
To find the number of ways to distribute 16 identical apples to your 6 favourite mathematics lecturers, we can use the stars and bars method. In this method, we imagine the apples as stars and the lecturers as bars. We need to distribute the 16 apples among the 6 lecturers in such a way that each lecturer gets at least 2 apples.
Since each lecturer needs to receive at least 2 apples, we can start by giving 2 apples to each lecturer. This leaves us with 16 - 2*6 = 4 apples to distribute. We can now distribute these 4 apples among the 6 lecturers using the stars and bars method.
Using the stars and bars method, the number of ways to distribute the remaining 4 apples among the 6 lecturers is (4+6-1) choose (6-1) = 9 choose 5 = 126. Therefore, there are 126 ways to give 16 identical apples to your 6 favourite mathematics lecturers, with each lecturer receiving at least 2 apples.