Fundamental Counting Principle
A family is hoping to have 4 kids. How many different combinations of gender could they have with those 4 kids?
2 x 2 x 2 x 2
16
5C5
1
4P4
24
What is the difference between a permutation and combination?
Order matters with permutations and it does not with combinations.
A restaurant is serving lunch, you get to pick 1 meat, 1 side and 1 drink. How many different combinations are there if the menu has the following...
Hot dog or Hamburger
Fries, Onion Rings, or a Pickle
Soda, Milk, or Water
2 x 3 x 3
18
In how many ways can 3 cards be selected from a standard deck of 52 cards?
52C3
22100
How many 4 letter permutations can be formed from the letters in the word RHOMBUS?
840
You are rolling a six-sided dice and recording the sum. (Ex: they both land on a 2 your sum is 4) Come up with the sample space of what you could roll.
S:{2, 3, 4 ,5, 6, 7, 8, 9, 10, 11, 12}
If a phone number has 7 digits and the first digit can not be zero how many different numbers can be made?
9 x 10 x 10 x 10 x 10 x 10 x 10
9,000,000
In how many ways can a student select five questions to answer from an exam containing nine questions?
9C5
126
An inspector must select three tests to perform in a certain order on a manufactured part. He has a choice of seven tests. How many different ways can he perform three tests?
7P3
210
A store is trying to advertise their 9 different detergents. In how many different orders could you display the detergents?
9!
362880
If you are dealt 4 cards how many different hands could you get?
52 x 51 x 50 x 49
6,497,400
A high school choir has 27 females and 19 males. Two students will be selected from the choir to represent the school All-State Choir. How many different pairs could they come up with?
46C2
1035
There are five violinists in an orchestra. Three of them will be selected to play in a trio with a different part for each musician. In how many ways can the trio be selected?
5P3
60
7 x 5 x 4
140
A ice cream shop has 5 flavors of ice cream. If you can get two scoops for you cone, and can double up on flavors how many different ice cream cones could you get?
5 x 5
25
A high school choir has 27 females and 19 males. Four students will be selected from the choir to represent the school All-State Choir. If there must be 2 of each gender how many different groups could they come up with?
27C2 and 19C2
351 x 171
60021
In how many ways can 4 raffle tickets be selected from 50 tickets if each of the 4 tickets wins a different prize?
50P4
5527200
What was the score of the Super Bowl?
49ers: 20
Chiefs: 31