Lark has forgotten her locker combination. It is a sequence of three numbers, each in the range from 1 to 30, inclusive. She knows that the first number is odd, the second number is even, and the third number is a multiple of 3. If the three numbers are different, how many combinations could possibly be Lark's?

Need __answer__**AND** ** explination** as soon as possible please!!! Thank you so much!!!!!!!!!!

Trinityvamp286
Jul 17, 2017

#1**+3 **

There are 15 odds from 1-30 inclusive

And there are 15 evens from 1-30 inclusive

It might be easiest to choose the last number, first

We have 5 odds that are multiples of 3 from 1-30 inclusive

Then we have 15 ways to choose the second even number

Finally, we have 14 ways to choose the first odd [ we have already chosen one of them as the last number ]

And we have 5 evens that are multiples of 3 from 1-30 inclusive

Then we have 15 ways to choose the second odd number

Finally, we have 14 ways to choose the first even [ we have already chosen one of them as the last number ]

So we have these two possibilities

( 14 odds ) ( 15 evens) (5 odds that are multiples of 3) = 750 combinations

(15 odds) (14 evens) ( 5 evens that are multiples of 3) = 750 combinations

So there are 750 + 750 = 1500 possible combinations

CPhill
Jul 17, 2017