tricolour ice cream

[binaras]

An ice cream factory produces only tricolor ice cream products, where each ice cream has 3 stripes of different colours. The factory uses the colours Pink, Purple, Yellow, Orange, Blue & Red (6 colours).
How many different ice cream products have at least one stripe out of the following colours - pink, purple or orange (Order does not matter)

The answer is 6 but need to understand the workings?

[GMATGuruNY]

"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.

[[email protected]]

Hi binaras,

You can see from Mitch's post that he's provided a question that is properly written, includes the answer choices AND includes the correct answer. Where did you find the question that you posted (what is the source?)? And why did you think the answer was 6? If the source is inconsistent or riddled with errors/typos, then you might want to invest in some different resources.

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

"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

We can use the formula:

Total number of ways to select 3 stripes - number of ways to select stripes without pink, purple or orange = number of ways with at least one of pink, purple or orange

Total number of ways to select 3 stripes:

6C3 = 6!/[3!(6-3)!] = 6!/(3!3!) = (6 x 5 x 4)/(3 x 2 x 1) = 20

The only way to choose 3 stripes, none of which is pink, purple, or orange, is if the 3 stripes are red, blue, and silver. Thus, the total number of ways to select stripes without pink, purple or orange:

3C3 = 1

So the number of ways with at least one of pink, purple or orange is 20 - 1 = 19.

Answer: D