Master Permutations for CBSE Class 11 Applied Mathematics. Learn fundamental counting principles, factorial notation, and arrangement problems with solutions.
If an event can occur in m ways and following it, a second event can occur in n ways, then the two events in succession can occur in m × n ways. This principle forms the basis of all permutation problems. It extends to any number of independent events occurring in sequence.
Step 1: Identify choices for each position. Hundreds place has 9 options (1-9), tens place has 10 (0-9), units place has 10 (0-9).
Step 2: Multiply the choices: 9 × 10 × 10.
Answer: 900
A permutation is an ordered arrangement of a set of objects. The number of ways to arrange n distinct objects taken r at a time is denoted by P(n, r). This formula accounts for the importance of the order of selection.
Step 1: Identify n=5, r=3.
Step 2: Use formula P(5, 3) = 5! / (5-3)! = 120 / 2.
Answer: 60
When some objects are not distinct, the number of arrangements decreases. If there are n objects where n₁ are of one type, n₂ of another, the total arrangements are adjusted by dividing by the factorials of the counts of identical items.
Step 1: Total letters n=5, 'P' repeats 2 times.
Step 2: Calculate 5! / 2! = 120 / 2.
Answer: 60