Master the Fundamental Principle of Counting for CBSE Class 11 Applied Mathematics. Learn Addition and Multiplication rules with solved examples.
If an event can occur in m ways and a second independent event can occur in n ways, then the sequence of the two events can occur in m × n ways. This principle extends to any number of events. For example, if you have 3 shirts and 4 trousers, you have 3 × 4 = 12 possible outfits.
Step 1: Identify choices for each position. Hundreds place: 9 choices (1-9).
Step 2: Tens place: 10 choices (0-9).
Step 3: Units place: 10 choices (0-9).
Answer: 9 × 10 × 10 = 900 numbers.
If an event can occur in m ways and another mutually exclusive event can occur in n ways, then either of the events can occur in m + n ways. This is used when events cannot happen simultaneously. For example, choosing one book from 5 Math books or 3 Physics books results in 5 + 3 = 8 choices.
Step 1: Identify groups. Group A has 12 students, Group B has 15 students.
Step 2: Since we pick one student from either group, add the possibilities.
Answer: 12 + 15 = 27 ways.
When counting arrangements with restrictions, always fill the restricted positions first. If a digit cannot be zero or must be even, handle that specific constraint before filling the remaining unrestricted positions. This ensures the multiplication principle is applied correctly to the remaining choices.
Step 1: Units place must be 0, 2, 4, 6, 8 (5 choices).
Step 2: Hundreds place cannot be 0 (9 choices).
Step 3: Tens place (10 choices).
Answer: 9 × 10 × 5 = 450.