MAIN COURSE PAGE This lesson summary covers counting arrangements and basic probability. Included is a lesson on basic sequences and series. See the math toolbox for additional, focused video lessons and related exercises. TestPrepSHSATKhan AcademyMath is FunTestPrepSHSATSequences & SeriesProbability & CombinationsProbability & Combinations Welcome to the PROBABILITY/COMBINATIONS/PERMUTATIONS instruction unit. These instructional quizzes are short, limited to only about a dozen questions, and they are not graded or timed. Occasionally there will be a question introducing a topic that you are not expected to answer at first. Do not panic. The instructional material will likely be introduced in the following answer explanation. The purpose of these instructional modules is to review subject material by topic that you will likely encounter on the exam and provide some topic specific tips to improve your ability to solve related problems. DO YOU KNOW WHAT THE COUNTING PRINCIPLE IS FOR INDEPENDENT EVENTS? YesNo Mary can drive or take a flight to NYC. From there she travels to Madrid and must choose from four available flights. Once in Madrid she can travel to her hotel by bus or taxi. How many different possible ways can Mary get to her hotel in Madrid? Please enter the numeric value and not any variation. e.g. '8' and NOT "eight' or '2 cubed', etc. There are 10 children in a class. How many ways can I line them up for recess? There are 10 students, 5 boys and 5 girls, in a class. How many ways can I line up the boys and girls for recess? There are 10 students in a class, 5 boys and 5 girls. How many ways can I sit them around a Harkness table? How many ways can the letters in the word STATISTICS be arranged? How many 3 digit numbers can be formed without repeating a digit? (002, 091 and the like are not considered 3 digit numbers for this purpose) 252648900999 There are 8 competitors for one event in the olympic games and only gold, silver, and bronze medals are awarded. How many possible combinations of medalists are there in this event? 856144336 What is the probability of rolling a 7 with two dice? (any roll of a singular die can result in a number 1 through 6 and "rolling a 7" means the sum of the numbers facing upward on both dice equals 7) 16.7%1/361/61/4 Do you think the chance of at least 2 students in your class having the same birthday is reasonably good or pretty low? Pretty LowReasonably Good What is the probability at least 2 students share a birthday in a class of 23 students? <5%5% up to, but not including 25%25% up to, but not including 50%>50% Which of the following is true? (check all that apply) Count the possibilities of several independent events occurring by multiplying the possibilities of each event. n unlike objects can be arranged n! ways.If r objects are alike then divide by r! to avoid over-counting.There are n!/(n-r)! ways to select r ordered objects from n total objects.There are n!/r!(n-r)! ways to select r objects from n total objects where order doesn't matter.Probability equals the number of ways an event can occur divided by the total possible outcomes, Khan AcademyKhan Academy (Sequences, Series, Probability) Arithmetic SequencesApproximately 20 minutes in several videos. Geometric SequencesApproximately 15 minutes in several videos. ProbabilityApproximately 10 minutes in several videos. Venn DiagramsApproximately 10 minutes in several videos. Compound ProbabilityApproximately 15 minutes video. Dependent ProbabilityApproximately 20 minutes in several videos. CombinationsApproximately 10 minute video. PermutationsApproximately 10 minute video. Basic Set OperationsApproximately 10 minutes 1st two videos. Math is FunMath Is Fun (Sequences, Series, Probability) SequencesArithmetic SequencesGeometric SequencesFibonacci SequencesInfinite SeriesProbabilityCounting PrincipleProbability ComplementProbability- Types of EventsCombinations & Permutations