College Math CLEP Prep Practice Exam

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How many possible five-number combinations can be made from the numbers 0 through 9 if each number can be used only once?

  1. 20

  2. 30

  3. 40

  4. 50

The correct answer is: 40

There are 10 available numbers to choose from and each combination must include five numbers, so the total number of possible combinations is the number of ways to pick 5 numbers from a set of 10, which is found using the formula nCr (n choose r) or n! / (r! * (n-r)!). Plugging in the values, we get 10! / (5! * (10-5)!) = 10!/ (5! * 5!) = (10*9*8*7*6) / (5*4*3*2*1) = 30240 / 120 = 252. Therefore, the correct answer is 252, which is not listed as an option. Option C, 40, is incorrect because it would be the correct answer if the number of available numbers was 8 instead of 10

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