Question

How do you calculate the complementary strand of a DNA strand? How do you calculate the number of different trinucleotides that can be made from one guanine, one uracil and one adenine?

Answer 1

I can give you the answer for the second part:

If you have three different items they can come in 6 different orders:
For small numbers you can write these out:
AGU-AUG-GAU-GUA-UAG-UGA, but you can think otherwise:

For the first you have three choices, for the second you have only two left, the the other one is fixed. Multiply these.

In general, if you have to calculate the number of orders of `n` different items, you have `n*(n-1)* (n-2)*....*2*1` possibilities.
This is also notated as `n!`, pronounced `n` factorial, it just means multiplying all numbers from `1` up to and including `n`.