Permutations and combinations are mathematical concepts used to count the number of possible outcomes in a given scenario.
Permutations are arrangements of objects in a specific order. For example, if you have three letters A, B, and C, the possible permutations are ABC, ACB, BAC, BCA, CAB, and CBA. The formula for finding the number of permutations is:
nPr = n! / (n-r)!
where n is the total number of objects and r is the number of objects being arranged.
Combinations, on the other hand, are arrangements of objects where order does not matter. For example, if you have three letters A, B, and C, the possible combinations are ABC, ACB, BAC, and CAB. The formula for finding the number of combinations is:
nCr = n! / (r! * (n-r)!)
where n is the total number of objects and r is the number of objects being selected.
To solve permutations and combinations problems, you need to identify whether the problem requires permutations or combinations, and then apply the appropriate formula. It is important to carefully read the problem and understand what is being asked before attempting to solve it.