Multiplication rule of counting
Jun 15, 2020, 16:45 IST
Multiplication rule of counting
Definition :-According to the multiplication rule, if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both 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 tasks A and B and C
= (p q r) ways.
Real life application :-
There are 3 flights from California to France, and 2 flights from France to India. Sanjeet wants to fly from California to France and then to India.
How many choices does he have for his flight plan?
3 WAYS X 2 WAYS = 6 WAYS
Example 1 :-You take a survey with five "yes" or "no" answers. How many different ways could you complete the survey?
Solution :-There are 5 stages: Question 1, question 2, question 3, question 4, and question 5.
There are 2 choices for each question (Yes or No).
There are 2 choices for each question (Yes or No).
So the total number of possible ways to answer is:
2 * 2 * 2 * 2 * 2 = 32.
Example 2 :-A company puts a code on each different product they sell. The code is made up of 3 numbers and 2 letters. How many different codes are possible?
Solution :-There are 5 stages (number 1, number 2, number 3, letter 1 and letter 2).
There are 10 possible numbers: 0 – 9.
There are 26 possible letters: A – Z.
So we have:
10 * 10 * 10 * 26 * 26 = 676000 possible codes.
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