# Statistics grocery store question

• Jun 16th 2012, 08:08 PM
u12480
Statistics grocery store question
Statistics Grocery Store Question
I am a new online Math Help Forum Friend. I'm back to school after many years out and am taking Statistics. I have a problem that I cannot seem to solve. Can you help?

A grocery produce manager inspects the corn supplied by a nearby farm. In a bushel of 30 ears of corn, the manager inspects 3 ears of corn. If 2 or more of the ears of corn are defective, the entire bushel is rejected. In this bushel, 5 ears of corn are defective. Find the number of ways that 2 or more ears of corn will be found defective by the produce manager.

Thank you.
• Jun 16th 2012, 08:26 PM
richard1234
Re: Statistics grocery store question
The bushel will be rejected in one of two ways:

Case 1: Exactly two ears are defective.
Case 2: Exactly three ears are defective.

Case 1: We want the number of ways to choose three ears of corn such that two of them are defective (given that 5/30 are defective). Here, we are choosing two defective ears out of five, and one normal ear out of the remaining 25. This can occur in $\displaystyle {{5}\choose{2}}{{25}\choose{1}} = 250$ ways.

Case 2: We want to pick all three defective ears out of the five. This can occur in $\displaystyle {{5}\choose{3}} = 10$ ways.

The total number of ways that two or more defective ears is chosen is $\displaystyle 250+10 = 260$.
• Jun 17th 2012, 04:08 AM
u12480
Re: Statistics grocery store question
Thank you Richard. This was very difficult for me and after several hours of working on it, I went searching for help. I appreciate
your writing out the explanation so that I can augment my learning.

Now I have yet another question. I can see that there is a 5 over 2 in parentheses and a 25 over 1 in parenthesis and a 5 over the 3 in parentheses. How do those numbers get worked in order to equal the sums you found?

Thank you.
• Jun 17th 2012, 07:27 AM
u12480
Re: Statistics grocery store question
I had one other question. Is there a name for the formula that you used to figure this out? Thank you.
• Jun 17th 2012, 09:36 AM
awkward
Re: Statistics grocery store question
The numbers in the funny parentheses are "binomial coefficients".

Binomial coefficient - Wikipedia, the free encyclopedia
• Jun 17th 2012, 10:29 AM
u12480
Re: Statistics grocery store question
So, if I haven't learned those yet is there another way to figure out this problem?
• Jun 17th 2012, 10:59 AM
Plato
Re: Statistics grocery store question
Quote:

Originally Posted by u12480
So, if I haven't learned those yet is there another way to figure out this problem?

If you have not had those yet, then you should not have been asked to do this question.
• Jun 17th 2012, 12:10 PM
richard1234
Re: Statistics grocery store question
Those are combinations, and they return binomial coefficients.

Basically, the number of ways to choose k objects out of a set of n (order doesn't matter, this is called a "combination") is denoted $\displaystyle {{n}\choose{k}}$ ("n choose k") and is given by

$\displaystyle {{n}\choose{k}} = \frac{n!}{(n-k)!k!}$.

For example, $\displaystyle {{5}\choose{2}} = \frac{5!}{3!2!} = \frac{120}{6(2)} = 10$
• Jun 17th 2012, 12:19 PM
u12480
Re: Statistics grocery store question
I appreciate your replies. We are just starting to do binomial equations. Thank you for the explanation.