There are 10 vehicles in a parking lot: 3 SUVs and 7 trucks. What is the probability that any 7 randomly chosen parking spots have 2 SUVs and 5 trucks OR 3 SUVs and 4 trucks?

Question

Mathematics

Mark Li

14 November, 16:41

There are 10 vehicles in a parking lot: 3 SUVs and 7 trucks. What is the probability that any 7 randomly chosen parking spots have 2 SUVs and 5 trucks OR 3 SUVs and 4 trucks?

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Santos Barr · Answer 1

We have to calculate the probability that any randomly choosen parking spots have 2 SUVs and 5 trucks or 3 SUVs and 4 trucks. We will use the formula with combinations: P = (3C2 * 7C5) / (10C7) + (3C3 * 4C7) / (10C7). For example: 10C7 = 10! / 7! * (10-7) ! = 10!/7!*3! = 10*9*8/3*2*1 = 120, etc. P = (3 * 21) / 120 + (1 * 35) / 120 = 63 / 120 + 35 / 120 = 98 / 120 = 0.8166. Answer: The probability is 0.8166 or 81.66%.