Combinatorics and Probability
Combinatorics can be very useful in calculating possible and favorable outcomes, especially for a large number of events.
Examples
1. A group of 10 people sit on a bench. What is the probability that two of the people decided in advance to sit together?
Possible outcomes:
Since the order matters and the elements are not repeated, there are permutations.
Favorable outcomes:
If the two people sitting together are considered as a single person there will be 9!, however, there can only be two possible forms for each of them, left or right, so there is 2 · 9!.
2.Five cards are drawn randomly from a standard deck consisting of 52 cards. Find the probability of picking:
4 aces.
Since the order does not matter and there are no repeated elements, there are combinations.
4 aces and 1 king.
3 fives and 2 jacks.
A 9, 10, jack, queen and king (in no particular order).
3 of any suit and 2 from another.
There are four ways of choosing the first suit and three ways of choosing to the second suit.
At least one ace.
