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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!!!!!!!!!!

Jul 17, 2017

#1
+94513
+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

Jul 17, 2017
#2
+56
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THANKYOU!!!

Trinityvamp286  Jul 17, 2017
#3
+95175
+1

Looks good to me too Chris :)

Melody  Jul 18, 2017
#4
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Thanks, Melody.....these counting problems always give me some trouble.....!!!

Jul 18, 2017