Final answer:
The number of permutations is calculated using factorial notation, with the formula n! for a set of n items. For independent events, multiply the possibilities or raise them to the power of repetitions.
Step-by-step explanation:
To calculate the number of permutations of a set of items, you use factorial notation, represented by an exclamation point (!). For example, to find how many ways you can arrange 4 items, you calculate 4!, which is equal to 4 × 3 × 2 × 1, resulting in 24 different combinations. No matter the size of the set, the pattern remains consistent: n! for n number of items. Permutations consider the order of arrangement to be important, thus every order counts as a unique combination.
For independent events, you can use multiplication to find the total number of permutations. If you want to determine the number of possible outcomes for multiple independent events, you raise the number of possibilities for a single event to the power of repetitions. For instance, choosing a card from a deck of 52 cards five times with replacement can be represented as 525 permutations.
In probability, to find the likelihood of specific outcomes, you would divide the number of favorable permutations by the total number of possible permutations. For example, the probability of drawing two red cards in a row from a shuffled deck can be calculated by dividing the number of ways to draw two reds by the total permutations of drawing any two cards.