Ways to assign nine accounts to three salesmen

Question

How many ways can nine accounts are assigned to three different salesmen so that each one gets three accounts? How many ways if one particular pair of accounts cannot be assigned to the same salesman?

Answer 1

Salesman 1: gets one of the two restricted accounts plus 2 of the other 7

Salesman 2: gets other restricted accounts plus 2 of the other 5

Salesman 3: gets the remaining 3 accounts

 

S1 # ways = 2 times 7C2 = 2(21) = 42

S2: # ways = 1 times 5C2 = 10

S3: # ways = 3C3 which is, of course, 1.

 

Answer is PRODUCT of these, namely 420.