Find probabilities using combinations and permutations

Learning Objectives Distinguish between scenarios requiring permutations (order matters) and combinations (order does not matter). Calculate the total number of outcomes in a sample space using permutation and combination formulas. Determine the number of favorable outcomes for a specific event. Apply the fundamental probability formula, P(E) = n(E) / n(S), to problems involving permutations and combinations. Solve probability problems related to selections, such as choosing a committee or a hand of cards. Solve probability problems related to arrangements, such as finishing positions in a race or arranging items on a shelf. Ever wonder what your actual chances are of winning the lottery or being dealt a perfect poker hand? 🃏 This lesson gives you the mathematical tools to...

TermDefinitionExample ProbabilityA measure of the likelihood of an event occurring, expressed as a ratio of favorable outcomes to the total number of possible outcomes.The probability of rolling a 4 on a standard six-sided die is 1/6, as there is one favorable outcome (rolling a 4) out of six total possible outcomes ({1, 2, 3, 4, 5, 6}). Sample Space (S)The set of all possible outcomes of a random experiment.When flipping two coins, the sample space is S = {HH, HT, TH, TT}. Event Space (E)A subset of the sample space, representing the set of outcomes that we consider favorable.In the experiment of flipping two coins, the event of getting at least one head is E = {HH, HT, TH}. PermutationAn arrangement of a set of objects in a specific order. Order matters.The permutations of the letters A...

Theoretical Probability Formula P(E) = n(E) / n(S) The probability of an event E is the number of outcomes in the event space, n(E), divided by the total number of outcomes in the sample space, n(S). Both n(E) and n(S) are calculated using the same counting method (either permutations or combinations). Permutation Formula nPr = n! / (n-r)! Use this to find the number of ways to arrange 'r' objects from a set of 'n' distinct objects. This is used for the numerator n(E) and/or denominator n(S) when the order of the outcomes is important. Combination Formula nCr = n! / (r! * (n-r)!) Use this to find the number of ways to choose 'r' objects from a set of 'n' distinct objects. This is used for the numerator n(E) and/or denominator n...