Maths help please

Question

1,3,5,6,7

 

the diagram shows five cars with different digits.find the number of three digit numbers that can be formed if:

 

the he sum of the digits is 9?????

Answer 1

It's not completely clear what the rules are. I assume you have to form 3-digit numbers from the digits on the cars.  And since the digits are shown on cars, I'd guess that the idea is to arrange the cars to show their numbers, which means that you can probably only use each digit once.  Is that correct?

 

If I'm right, then notice that the only way you can get 3 of the digits to add up to 9 is by using 1, 3, and 5.  If you use 6, then you'd need the other 2 digits to add up to 3.  But there's no way to get 3 using 2 of the other cars.  And the same is true if you use 7.

 

So then the question is, how many ways can you arrange 1, 3 and 5?  I'm not sure if you've learned about permutations yet.  If you have, then the answer is just 3! = 6, since you're arranging 3 objects in a way where the order counts.

 

If you haven't learned about permutations, then you can just solve the problem by doing the arranging manually.  That is, set up all the 3-digit numbers that have a 1, a 3, and a 5:

 

135

153

315

351

513

531

 

That's all of them, and again the answer is 6.