Permutation and Combination

Permutation and combination provide tools for determining the likelihood of events and outcomes in various scenarios.

Permutation refers to the arrangement of items in a specific order without repetition.

The word "APPLE" has 5 letters, and there are 5! (factorial) ways to arrange them without repetition.

Each prize can be awarded to any of the 10 participants, resulting in 10 choices for the first prize, 9 choices for the second prize, and 8 choices for the third prize. Therefore, the total number of ways is 10 * 9 * 8 = 720.

Without repetition, each digit can only be used once. Thus, there are 4 choices for the first digit, 3 choices for the second digit, and 2 choices for the third digit, resulting in 4 * 3 * 2 = 24 possibilities.

The number of ways to select a group of 5 people from a total of 12 people is given by the combination formula C(12, 5) = 12! / (5! * (12-5)!