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Hello my name is Professor Liam. Today I will be teaching you about the math concept, combinations. The definition of combinations is, a joining or merging of different parts or qualities in which the component elements are individually distinct. So an example of this would be a license plate. To see how many combinations you can possibly have on your license plate you would multiply the amount of possible outcomes each letter or number can be. My car is registered under California so I will use that as an example. A California license plate has 7 letters and numbers. It starts out with one number then continues with 3 letters then has 3 other numbers. So to figure out how many combinations I can possibly have for a California license plate I would multiply 10, because I can have 10 possible numbers in the first place, by 26, because of 26 letters in the alphabet, by 26, by 26, by 10, by 10, by 10. The equation would look like this:

10*26*26*26*10*10*10

This gives an answer of 175,760,000 possible combinations for a California license plate.

If license plate could not have repeating numbers and letters than I would have the equation 10 times 26 times 25, because I couldn't use the previous letter, times 24, because I couldn't use both the previous letters, time 9, because I couldn't use the number in the first space, times 8, times 7. This process is called combination without replacement because you are not placing the previous letter or number back into the possible numbers or letter that could be chosen for the next letter or number. The equation for a license plate without replacement would be:

10*26*25*24*9*8*7

This gives an answer of 78,624,000 possible combination for a California license plate without combination.


Thank you for coming to class.