At a particular pizza shop, a pizza can be created from any combination of 3 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?  Choose the correct choice from the following:
A) 6
B) 35
C) 120
D) 450
E) 740
Number of possible ways to select 1 type of spice = 3c1 = 3   Number of possible ways to select 2 types of cheese = 4c2 = 6   (Here we can pick our answer as 450- 450 since it is the only answer that is divisible by   3*6= 
<gadget id="calculator">  3*6</gadget>
<output>18</output>
18 , but most likely on the GMAT there will be more another answer that will be divisible by 18 )   Number of possible ways to select 4 types of meat but without pepperoni and anchovies together= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together   = 7c4 - 5c2   =35 - 10= 
<gadget id="calculator">35 - 10</gadget>
<output>25</output>
25   Possible ways to garnish the pizza are available to the customer= 3*6 * 25= 
<gadget id="calculator">3*6 * 25</gadget>
<output>450</output>
450   Answer 450
<result>D</result>
At a particular pizza shop, a pizza can be created from any combination of 3 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?