SOLUTION: The combination locks on the lockers at Hillside School have numbers from 0 through 39 (inclusive). A locker combination consists of three different numbers, where order matters. B

Question 1180836: The combination locks on the lockers at Hillside School have numbers from 0 through 39 (inclusive). A locker combination consists of three different numbers, where order matters. Because of the way the locks are manufactured, all three numbers are even or all three numbers are odd. How many combinations are possible?
So I think that to get ALL the possible combinations you do 40P3 which is 40 times 39 times 38 = 59280, but I don't know what to do after that.
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!



There are 20 even numbers (0,2,4,...,38) and 20 odd numbers (1,3,...,39)



There are two cases: the numbers are all odd or they are all even.  You will need to add them together:



If the numbers are odd, you get 20*19*18

If the numbers are even, you get 20*19*18



So the total number of combinations is  2(20*19*18) = 13680

 

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