+0  
 
0
65
1
avatar

In how many ways can three distinct numbers be chosen from the set {1, 2, 3, ..., 9}, so that their sum is a multiple of 3?

 Jul 1, 2020
 #1
avatar+21953 
0

Start listing them (have the second digit larger than the first and the third digit larger than the second):

123     126     129     135     138     147     156     159     168

234     237     246     249     258     267     279

345     348     357     369     378    

456     459     468    489

567     579

678

789

But each of these can be chosen in 6 ways:   123  =  132  =  213  =  231  =  312  =  321

 

So take the number of ways listed and multiply by 6.

 

It would also be wise to check to see if I have missed any.

 Jul 1, 2020

13 Online Users

avatar
avatar