Generalized Permuations and Combinations

Repetitions, Indistinguishable Objects, and Objects in Boxes

Indistinguishable Objects

E X A M P L E S

Basic Application | Advanced Application

Example: Basic Application

How many different strings can be made using all the letters from ABRACADABRA? This is very similar to the example earlier in the tutorial. Again, we identify all the unique objects: (5) A (2) B (1) C (1) D (2) R Apply what we know of the formula, n = 11, n1 = 5, n2 = 2, n3 = 1, n4 = 1, and n5 = 2. Therefore, the number of different strings is = 11! 5! 2! 1! 1! 2! = 83,160

Return to tutorial: Indistinguishable Objects

Example: Advanced Application

Stranded on a desert island with nothing but your Discrete Mathematics textbook, you stumble across a cahce of tropical fruit. You discover 3 kumkwats, 4 avacados, and 2 pugnacious pomegranates. To nourish your mind and body, you decide to figure out how many different orders you can eat the fruit. Applying the 'Indistinguishable Objects' formula, you determine that n = 9, n1 = 3, n2 = 4, and n3 = 2. So, the number of different orders to eat the fruit are = 9! 3! 4! 2! = 1260