Combinatorics and Probability
Combinatorics can be very useful in calculating possible and favorable outcomes, especially for a large number of events.
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?
Since the order matters and the elements are not repeated, there are permutations.
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:
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.