Arrangements of Like and Unlike Objects An arrangement is a sequence of elements in which the order of the elements matters. For example, the arrangements o...
Arrangements of Like and Unlike Objects
An arrangement is a sequence of elements in which the order of the elements matters. For example, the arrangements of the letters in the word "apple" are different from the arrangements of the letters in the word "applets".
A permutation is an arrangement in which the order of the elements matters. For example, the permutations of the letters in the word "apple" are different from the permutations of the letters in the word "aplpec".
A combination is an arrangement in which the order of the elements does not matter. For example, the combinations of the letters in the word "apple" are the same as the combinations of the letters in the word "aplpec".
The number of arrangements of n elements is n! (n factorial). The number of permutations of n elements is n! / (n-r)! (r factorial), where r is a positive integer. The number of combinations of n elements is n! / r! (r factorial).
For example, the number of arrangements of 5 elements is 5! = 120. The number of permutations of 5 elements is 5! / (5-3)! = 120. The number of combinations of 5 elements is 5! / 5! = 1