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sawarealire.com 12-3 Enrichment Permutations and Combinations Maya claims that, in a class of 30 students, there is a greater than 50% chance that at least 2 students have the same birthdate. Can this claim be true? If P(n) = P(n students have the same birthday), then P(n) = P(1) + P(2) + P(3) + ... P(n). That would be a tedious calculation indeed! So, let P(1) = P(each student's birthdate is unique) and P(n 2 2) = P(2 or more students have the same birthday) and find P(1). Complete Items 1-6 to see if you agree with Maya's claim. 1. How are P(n 2 2) and P(1) are related? Complete the equation with the appropriate symbols. P(n 2 2) 100% For Items 2-5, complete each expression. Then evaluate the expressions for Exercises 4-5, using a calculator. (You may need to rewrite the expression for your calculator.) Assume 365 days in the year. Question Expression Answer 2 How many ways are there for 30 people to all have different birthdays? 3 How many possible sets of birthdates are there for 30 people? 4 What is All. the approximate probability that each of the 30 birthdays is unique, to the nearest whole percent