Answer:
[tex]C^{18}_6\cdot C^{12}_6=17,153,136[/tex]
Step-by-step explanation:
Joe, Megan, and Santana are salespeople. Their sales manager has 18 accounts and must assign six accounts to each of them.
1. Sales manager can assign first six accounts in
[tex]C^{18}_6=\dfrac{18!}{6!(18-6)!}=\dfrac{12!\cdot 13\cdot 14\cdot 15\cdot 16\cdot 17\cdot 18}{2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 12!}=\dfrac{13\cdot 14\cdot 15\cdot 16\cdot 17\cdot 18}{2\cdot 3\cdot 4\cdot 5\cdot 6}=18,564[/tex]
different ways.
2. Then 12 accounts left and he can assign the next 6 accounts in
[tex]C^{12}_6=\dfrac{12!}{6!\cdot (12-6)!}=\dfrac{6!\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{6!\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6}=\dfrac{7\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{2\cdot 3\cdot 4\cdot 5\cdot 6}=924[/tex]
different ways
3. Last 6 accounts he will assign in 1 way.
Hence, the total number of ways is
[tex]C^{18}_6\cdot C^{12}_6=18,564\cdot 924=17,153,136[/tex]
