The Fundamental Principle of Counting is also known as the counting rule to find the total number of possible ways or outcomes.
The fundamental principle of summation:
If a work A can be done in m ways and another work B can be done in n ways then work A or B can be done in m + n ways.
Consider total n works, if 1st work can be done in a, ways, 2nd work can be done in a way, and so on nth can be done in a way then work a, or a, or …or a, can be done in a + a + … + a way.
Example:
If Aron has one sandal, one formal shoe, and one sports shoe, in how many ways he can select his footwear?
Solution:
Since a person can wear only one piece of footwear at a time, he can wear either sandals or formal shoes or sports shoes, which means he has a total of 3 ways to select his footwear.
Example:
Trina went to a famous restaurant for dinner, there in the menu card she saw 10 Indian and 12 Chinese food, in how many ways she can select?
Solution:
The number of ways that she can select Indian food is 10 and the number of ways that she can choose Chinese food is 12 but she is allowed to have either Indian or Chinese food hence the number of ways that she can select food is 10+12=22 ways.
The fundamental principle of multiplication:
If work A can be done in m ways and another work B can be done in n ways then work A & B can be done in m x n ways.
Consider total n works, if 1st work can be done in a way, 2nd work can be done in a way, and so on nth can be done in a way then work a, a, …,a, a, can be done in a x a, x… x a way.
Example:
If Rajesh has 4 formal shirts and 5 formal trousers, how many ways can he wear his dress?
Solution:
Rajesh can select shirts in 4 ways and trousers in 5 ways hence the number of ways he can select his dress is 4 x 5 = 20
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