SOLUTION: how many 6 number combinations will be made from 1 2 3 4 5 6 7 8 9, where 1 2 and 3 must appear on the 6-number combination?

Algebra ->  Permutations -> SOLUTION: how many 6 number combinations will be made from 1 2 3 4 5 6 7 8 9, where 1 2 and 3 must appear on the 6-number combination?      Log On


   

Question 26342: how many 6 number combinations will be made from 1 2 3 4 5 6 7 8 9, where 1 2 and 3 must appear on the 6-number combination?
Found 2 solutions by venugopalramana, Levski123:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
1,2 AND 3 MUST APPEAR IN THE COMBINATION.
SO WE NEED TO SELECT ANOTHER 3 NUMBERS ONLY OUT OF REMAINING 6 NUMBERS WHICH CAN BE DONE IN 6C3 WAYS
6C3=6*5*4/(3*2*1)=20

Answer by Levski123(6) About Me  (Show Source):
You can put this solution on YOUR website!
Because 1,2,3 must be in the 6 digits we only need to worry about 3 other digits, and how many possible combinations there for them. There are 9 possible digits and we are taking 3 at a time (remember we are working with combinations, order does not matter) So there are 9C3 combinations for the remaining three digits. When we combine all the possible combinations we get 1x1x1x9C3 to get the total 84 combinations