Combination regular formula with the seprate events

when we talk about "separate events," we're delving into the realm of probability and combinatorics where different events or processes are independent.

For instance, if you want to find the number of ways to choose 2 books from a set of 5 and 3 pens from a set of 7, you can't simply use the combination formula directly. Each of these is a separate event:

Choosing 2 books from 5: C(5,2)
Choosing 3 pens from 7: C(7,3)
To find the total number of ways to do both events simultaneously, you'd multiply the number of ways for each event:

Total ways=C(5,2)×C(7,3)
This is because for each way to choose 2 books, there are C(7,3) C(7,3) ways to choose 3 pens, so the events are combined multiplicative.

So, to answer your question: The regular combination formula applies to situations where you're selecting items from a single set. When you have separate events or selections from different sets, you typically need to compute combinations for each event separately and then combine them using the rules of counting (like multiplication for independent events).