1. Product Rule
The product rule for counting in combinatorics is a technique for calculating the total number of possible selections from a set or sets of objects.
1.1 How to apply Product Rule for Counting?
In order to use the product rule for counting, we use the following steps:
- Observe and identify the number of sets to be selected.
- Identify how many items to select from each set.
- Multiply the number of items in each set.
If selecting two items from a set,
- Calculate n x (n - 1) …if order does not matter
- Calculate
… if order matters
Example: A cafeteria menu has four different starters, three different mains, and five different dessert options. How many different ways are there to choose a starter, a main, and a dessert?
Solution:
Example: Tripti is trying to pick two fruits in a party. She must decide which fruit will she eat first and which one second. If there are 24 fruits to choose from, how many different options does she have?
Solution:
Example: 12 teams must play cricket with each other once. How many matches in total will be played?
Solution:
