Combinatorics Flashcards
What is the name of the principle where at least x amount of y must be in at least x amount of holes?
The Pigeonhole principle.
A circular table has n amount of people sitting at the table. How many possible arrangements of this table are possible?
There are (n-1)! arrangements possible.
There is a line of 8 people waiting for a bus. In this line, there are 4 boys and 4 girls. How many ways can the boys and girls alternate in this line?
8!/(4!x4!) = 8 factorial divided by 4 factorial squared = 40320/576 = 70 ways.
There are 15 pigeons and 121 pigeonholes. Explain why there will be at least 9 pigeons in at least one pigeonhole.
There will be at least 9 pigeons in at least one pigeonhole as in a situation where the pigeons are spread evenly, there will be 8 pigeons in 14 holes and 9 pigeons in one hole. [(121/15) > 8]
There are 25 people trialling for a football team. In this football team, there are 15 available selections. How many different arrangements of people are there to be chosen for this team.
25C15 or 25 choose 15.
How many different ways can you rearrange the letters in WOOLLOOMOOLOO to create 13 letter words?
13!/(8! x 3!) = 6227020800/241920 = 25740 ways.
Find the probability that one club and two hearts are dealt in any order. (Standard deck of cards)
(13C1 x 13C2)/52C3 = 39/850
Explain how there is no difference in the equations: 10C2 and 10C8
There is no difference in the equations 10C2 and 10C8 as in both situations you are creating a group of 2 people and 8 people, resulting in the same groups.
There are 2 lines of 4 people standing next to each other. Albert and Bertha ask to stand next each to other in the left line. How many arrangements of people are there?
3! x 4! = 144 ways
A quiz consists of 20 questions, each taking the answer yes or no. How many ways is it possible to get 13 correct and 7 incorrect answers?
20C13 or 20 choose 13 = 77520
