Multiplication law:
If one experiment has n probable outcomes and other experiment has m probable outcomes, then there are m x n probable outcomes when both of these experiments are happened.
Example :A college provides 7 courses in the morning and 5 in the evening. Calculate the possible number of selection with the student if he needs to study one course in the morning and one in the evening.
Solution: The student has seven selections from the morning courses out of which he may choose one course in 7 types.
For the evening part, he has 5 selections out of which he may choose one in 5 types.
Therefore the total number of types in which he may make the selection of one course in the morning and one in the evening = 7 x 5 = 35.
Example: A person needs to go from station A to station C via station B. There are three paths from A to B and four ways from B to C. In how various ways may he travel from A to C?
Solution: A → B in 3 ways
B → C in 4 ways
⇔ A → C in 3 x 4 = 12 ways
Remark:
The principle of multiplication is applicable only when the number of types of doing every part is independent of one other i.e. related to any function of doing the first part, the another part may be done by any function.
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