In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least two of each type of coin must be included?	Choose the correct choice from the following answers
A) 0 B) 9 C) 12 D) 15 E) 73
I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any dimes. We can't have all four coins represented if we have four quarters.   II. Case II = Three Quarters (75 cents)   Two dimes and two nickels would bring us up to $1.05, and we wouldn't have any pennies.   III. Case III = Two Quarters (50 cents)   This allows for 2-4 dimes.   Subcase 1 = 2 Q, 4 D (90 cents)   (1 way) two nickels allows for 5 pennies   Subcase 2 = 2 Q, 3 D (80 cents)   (3 ways) we could have 2-4 nickels   Subcase 3 = 2 Q, 2 D (70 cents)   (5 ways) we could have 2-6 nickels   Case III allows for a total of 9 ways   There's no other case, because we have to have at least two quarters and two dimes. The total over the cases equals   Total = 0 + 0 + 9= 
<gadget id="calculator">0 + 0 + 9</gadget>
<output>9</output>
9 ways.   OA=(9)
<result>B</result>
In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least two of each type of coin must be included?