Addition rule of counting

Jun 15, 2020, 16:45 IST

Addition rule of counting

Definition :-According to the addition rule if we have A ways of doing something and B ways of doing another thing and we cannot do both at the same time, then there are A + B ways to choose one of the actions.

Discription of formula :-
If a task A can be done in p ways
If a task B can be done in q ways
If a task C can be done in r ways
Then number of ways of doing either task A or B or C
= (p + q + r) ways

Real life application :-A person has 3 different black color shirt, 4 blue color and 5 white color shirt then the number of ways of wearing a shirt is
3 ways + 4 ways + 5 ways = 12 ways

Example 1 :-Jacob goes to a shop to buy some ping pong balls. He wishes to choose one ball from the amateur section, which had a total of five balls; or one ball from the professional section, which had a total of three balls. How many ways are possible in which he can buy a ball i.e. he can buy one ball from the amateur section OR one ball from the professional section?

Solution :-n(Jacob buying a ball) = n(Jacob buys one ball from the amateur section) + n(Jacob buys one ball from the professional section)
n(Jacob buying a ball) = = 5 + 3 = 8

Thus there are 8 possible ways in which Jacob can buy a ball from the store, according to his specific wishes.

Example 2 :-Ravi goes to a pet shop and finds that the pet shop has 33 reptiles, 44 birds, 55 rabbits, and 66 fish. If Ravi can only pick one animal as a pet, how many choices does Ravi have for a pet?

Solution :-Since Ravi can choose a reptile, or a bird, or a rabbit, or a fish, the rule of sum applies. Then
• there are 33 ways to select a reptile;
• there are 44 ways to select a bird;
• there are 55 ways to select a rabbit;
• there are 66 ways to select a fish.
By the rule of sum, there are 3+4+5+6=183+4+5+6=18 ways to select a pet.