Let’s count – Counting unions, 2

Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the complete solution of the exercises in the video or in the pdf below.

Exercise 2.

In how many ways can one form a sequence of length $5$ using an alphabet of 3 letters if the sequence is to have at least two consecutive equal letters?

Exercise 3.

In how many ways is it possible to give a child 16 jelly beans when choosing from a large bin containing (at least 13 of each type) lemon, mint, and raspberry jelly beans if the child is to receive exactly 3 of at least one of the flavors?