Create your own sundae:
12 ice Cream Flavors
10 Kinds of Candies
8 Liquid Toppings
5 Kinds of Nuts
With or Without Whipped Cream
If a customer makes exactly one selection from each of the five categories shown in the above table, what is the greatest possible number of different ice cream sundaes that a customer can create?
I know it is a combination problem, 5 from 37. But how to ensure 1 from 12, 1 from 10, 1 from 8, 1 from 5 and 1 out of 2??
Combination Problem : Need Help
This topic has expert replies
-
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Fri Mar 06, 2009 7:24 am
- Location: India
- Thanked: 1 times
The man who lets a leader prescribe his course is a wreck being towed to the scrap heap.
- Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
Hi!cnseetharaman wrote:Create your own sundae:
12 ice Cream Flavors
10 Kinds of Candies
8 Liquid Toppings
5 Kinds of Nuts
With or Without Whipped Cream
If a customer makes exactly one selection from each of the five categories shown in the above table, what is the greatest possible number of different ice cream sundaes that a customer can create?
I know it is a combination problem, 5 from 37. But how to ensure 1 from 12, 1 from 10, 1 from 8, 1 from 5 and 1 out of 2??
The question is actually much easier than you think. Let's start with a simpler version of the same question:
Solving by brute force, we get:John is going to pick one appetizer and one main course for his meal. If the only appetizers available are salad and soup and the only main courses are fish, beef and chicken, how many different meals could John choose?
Salad/Fish
Salad/Chicken
Salad/Beef
Soup/Fish
Soup/Chicken
Soup/Beef
for a total of 6 possible meals.
However, what we're really doing is picking one selection out of the two possibilities for each course. So, in terms of combinatorics we have:
Appetizers: 2C1 = 2
Main Courses: 3C1 = 3
Here's one of the most important thing to remember about combinations, permutations and probability:
if you're counting MULTIPLE possibilities, MULTIPLY the individual possibilities;
and
if you're counting ALTERNATIVE possibilities, ADD the individual possibilities.
Here, we're choosing one appetizer AND one main course, so we MULTIPLY:
2C1 * 3C1 = 2*3 = 6
Now, back to your question:
Each sundae consists of one flavour AND one candy AND one liquid AND one nut AND with/without whipped cream. So, we count the number of possibilities from each category and MULTIPLY them together.
Flavour: 12C1 = 12
Candy: 10C1 = 10
Liquid: 8C1 = 8
Nuts: 5C1 = 5
With/without whipped cream: 2C1 = 2
Accordingly, we have 12*10*8*5*2 = 120*8*10 = 1200*8 = 9600 different possible sundaes!
If you're not sure what exactly "12C1" (read as "twelve choose one") means, then you need to brush up on your combinatronics - but you really don't need to know any fancy math to realize that if there are 12 options and you're going to choose exactly 1 of them there are 12 possible choices.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
-
- Junior | Next Rank: 30 Posts
- Posts: 16
- Joined: Wed Mar 18, 2009 10:28 am
The number of ways he can choose 1 Ice cream flaovor is = 12C1 = 12.cnseetharaman wrote:Create your own sundae:
12 ice Cream Flavors
10 Kinds of Candies
8 Liquid Toppings
5 Kinds of Nuts
With or Without Whipped Cream
If a customer makes exactly one selection from each of the five categories shown in the above table, what is the greatest possible number of different ice cream sundaes that a customer can create?
I know it is a combination problem, 5 from 37. But how to ensure 1 from 12, 1 from 10, 1 from 8, 1 from 5 and 1 out of 2??
So, it boils down to a multiplication of all the categories.
Number of Different Ice Cream Sundaes = 12*10*8*5*2 = 9600.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7242
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The total number of options are:cnseetharaman wrote:Create your own sundae:
12 ice Cream Flavors
10 Kinds of Candies
8 Liquid Toppings
5 Kinds of Nuts
With or Without Whipped Cream
If a customer makes exactly one selection from each of the five categories shown in the above table, what is the greatest possible number of different ice cream sundaes that a customer can create?
12 x 10 x 8 x 5 x 2 = 9,600
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews