Permutation, Combination & Probability: Comprehensive Notes and 100 Practice Questions with Answers
Permutation, Combination & Probability: Comprehensive Notes and 100 Practice Questions with Answers 1. Counting Principles A. Fundamental Principle of Counting If an event can occur in m m ways and another in n n ways, both can occur in m × n m × n ways. Example: If you have 3 shirts and 2 pants, you can dress in 3 × 2 = 6 3 × 2 = 6 ways. 2. Permutations A. Definition Permutation is an arrangement of objects where the order matters 1 4 6 . B. Formulae Without Repetition: n P r = n ! ( n − r ) ! n P r = ( n − r )! n ! With Repetition: n r n r (Each of the r r positions can be filled in n n ways.) C. Examples Arranging 3 books on a shelf: 3 ! = 6 3 ! = 6 ways. Arranging 2 out of 5 people in a line: 5 P 2 = 5 × 4 = 20 5 P 2 = 5 × 4 = 20 ways 1 6 . 5-digit number with no repeated digits: 10 P 5 = 30 , 240 10 P 5 = 30 , 240 ways 2 . 3. Combinations A. Definiti...