Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GREEN. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?	Choose the most appropriate option.
A) 12
B) 14
C) 18
D) 19
E) 20
IMO: D - 19   There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, GREEN) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.   The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).   #1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3= 
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
9   #2: Pick two out of PPO and one out of SBP: 3C2 * 3C1= 3 * 3= 
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
9   #3: Pick three out of PPO: 3C3= 1   9 + 9 + 1= 
<gadget id="calculator">9 + 9 + 1</gadget>
<output>19</output>
19   answer is 19
<result>D</result>
Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GREEN. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?