tricolour ice cream

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

binaras: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Sat Jun 21, 2014 10:31 pm; Followed by:1 members

tricolour ice cream

by binaras » Fri Mar 11, 2016 1:18 am

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?

Quote

Source: Beat The GMAT — Problem Solving | Fri Mar 11, 2016 1:18 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Fri Mar 11, 2016 2:48 am

"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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Quote

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Fri Mar 11, 2016 9:45 am

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

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 14, 2018 10:08 am

"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

Scott Woodbury-Stewart
Founder and CEO
[email protected]