Melissa R.

asked • 05/19/17

Combination help

While walking down the street, you see an apple vendor, who has 11 apples for sale, but 3 of them are rotten. If you decide to buy 3 apples, how many ways can you buy at least 1 rotten apple?

1 Expert Answer

By:

Kemal G. answered • 05/19/17

Tutor
4.8 (5)

Patient and Knowledgeable Math and Science Tutor with PhD

See tutors like this
See tutors like this
Hi Melissa,
 
This would be combinations of three out of 11.
C(11 3) = 11!/((11-3)!*3!)
= 11*10*9*8! / (8!*3*2*1)
= 165
 
 
Upvote • 0 Downvote
More
Report

Kemal G.

Hi Melissa,
 
The answer I provided lists the number of all possible samples of three. However, the question is asking for the possible number of ways that one can buy at least one rotten apple in a sample of three.
 
This involves considering cases where you buy one, two or three rotten apples. 
There are 11 apples. Three are rotten so eight will be good.
These different cases can be calculated as below:
number of ways of buying one rotten apple = C(3, 1)C(8, 2) = 3*28 = 54
number of ways of buying two rotten apples = C(3, 2)C(8, 1) = 3*8 = 24
number of ways of buying three rotten apples = C(3, 3)C(8, 0) = 1*1 = 1
We need to add them up. 
54+24+1 = 79 possible ways of buying at least one rotten apple in a sample of three
 
 
 
Report

05/19/17

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.