Combinations of 7 pencils, 5 ball-points, and 2 felt-tips

[Fiona09]

A student has a cup with 14 writing implements: 7 pencils, 5 ball point pens, and 2 felt-tip pens.

In how many ways can the student select 4 writing implements? = C(14,4) = 1001

In how many ways can the selection be made if no more than one ball point pen is selected?

I cannot seem to figure out how to answer the second part to this problem. Everything I try keeps leading back to this:

C(14,4) - C(9,3) X C(5,1), which is incorrect but seems logical to me. I am new to these types of problems and would really appreciate any help you are willing to provide. Thanks!

 

[Deleted member 4993]

Re: Combinations Problem

A student has a cup with 14 writing implements: 7 pencils, 5 ball point pens, and 2 felt-tip pens.

In how many ways can the student select 4 writing implements? = C(14,4) = 1001

In how many ways can the selection be made if no more than one ball point pen is selected?

I cannot seem to figure out how to answer the second part to this problem. Everything I try keeps leading back to this:

C(14,4) - C(9,3) X C(5,1), which is incorrect but seems logical to me. I am new to these types of problems and would really appreciate any help you are willing to provide. Thanks!

No more than 1 means:

0 ball point pen [C(9,4)] + 1 ball point pen [C(9,3)*C(5,1)] <<< edited

 

[Fiona09]

So, according to your formula, the answer should be 630? If that is so.... it is incorrect. However, I probably worked it out wrong or just misunderstood you. Is there any other way you could break it down for me? I have an exam coming up shortly and would really benefit by understanding how to work these types of problems. Thanks!

 

[Deleted member 4993]

So, according to your formula, the answer should be 630? If that is so.... it is incorrect.

No....

It is

126 + 84*5 = 546


However, I probably worked it out wrong or just misunderstood you. Is there any other way you could break it down for me? I have an exam coming up shortly and would really benefit by understanding how to work these types of problems. Thanks!

 

[Fiona09]

Hello, thank you for responding so quickly. I plugged 756 into my Webwork (Homework online) and it was incorrect. Any other ideas on how to tackle this problem?

 

[Deleted member 4993]

Sorry - I had some mistakes.

Check my corrections above.