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EXAMPLE 3 Find a probability using permutations For a town parade, you will ride on a float with your soccer team. There are 12 floats in the parade, and their order is chosen at random. Find the probability that your float is first and the float with the school chorus is second. PARADE SOLUTION STEP 1 Write the number of possible outcomes as the number of permutations of the 12 floats in the parade. This is 12 P 12 = 12!.

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EXAMPLE 3 Find a probability using permutations Write the number of favorable outcomes as the number of permutations of the other floats, given that the soccer team is first and the chorus is second. This is 10 P 10 = 10!. STEP 2 STEP 3 Calculate the probability. soccer team is first chorus is second P ( ) = 10! 12! Form a ratio of favorable to possible outcomes. = 10! 12 11 10! Expand factorials. Divide out common factor, 10!. 1 = 132 Simplify.

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GUIDED PRACTICE for Example 3 4. WHAT IF? In Example 3, suppose there are 14 floats in the parade. Find the probability that the soccer team is first and the chorus is second. ANSWER 1 182

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