Question

The numbers 1, 2, 3, 4, 5, and 6 are placed in a line. How many even numbers can be made from these digits?

Answer 1

Answer:    360

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Explanation:

We have 3 even values (2,4, and 6) so this is the number of choices we have for the units digit. Recall that a number is even if the units digit is 0,2,4,6 or 8.

Once we have the units digit selected, we have 6-1 = 5 choices for the first slot, 6-2 = 4 choices for the second slot, and so on until we get down to 6-5 = 1 choice for the fifth slot

We could write it out like this

• slot one = 5 choices
• slot two = 4 choices
• slot three = 3 choices
• slot four = 2 choices
• slot five = 1 choice
• slot six = units digit = 3 choices

Multiply those values out: 5*4*3*2*1*3 = 360

There are 360 different even numbers possible.