"Ice-Cold" Ice-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 red. 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)?
A. 12
B. 14
C. 18
D. 19
E. 20
Good products = total products - bad products.
Total products:
From 6 flavors, the number of ways to choose 3 to form a stripe = 6C3 = (6*5*4)/(3*2*1) = 20.
Bad products:
A bad product does not include pink, purple or orange.
Only ONE combination of 3 colors does not include pink, purple or orange:
yellow, blue, red.
Subtracting the 1 bad product from the 20 possible products, we get:
Good products = 20-1 = 19.
The correct answer is
D.
Last edited by GMATGuruNY on Fri Mar 11, 2016 10:48 am, edited 1 time in total.
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