# Past exam questions help

• Feb 16th 2011, 01:57 PM
smallfry
Past exam questions help
Hi,

There is one question I don't understand.

A bin contains 5 matched pairs of gloves. Each matched pair contains a left hand and a right hand glove that match. In how many ways can 4 gloves be taken from the bin without including a matched pair?

Possible answers: 160, 120, 80, 40, 30
• Feb 16th 2011, 02:03 PM
dwsmith
Quote:

Originally Posted by smallfry
Hi,

My professor posted some past exam questions, but didn't post the answers to them :(

Can anyone tell me if my answers are right?

And for #2, I have no clue what the answer is, so that one is the most important!

(click it to make it bigger)

http://img248.imageshack.us/img248/9379/pastexam.png

Thanks!

Too many questions in one thread.
• Feb 16th 2011, 03:56 PM
smallfry
Quote:

Originally Posted by dwsmith
Too many questions in one thread.

Sorry :( I'm pretty sure about most of them except number 2... I'm gonna edit the thread to contain only it.
• Feb 16th 2011, 05:30 PM
Prove It
Quote:

Originally Posted by smallfry
Hi,

There is one question I don't understand.

A bin contains 5 matched pairs of gloves. Each matched pair contains a left hand and a right hand glove that match. In how many ways can 4 gloves be taken from the bin without including a matched pair?

Possible answers: 160, 120, 80, 40, 30

Since there are 5 pairs of gloves, there are 10 gloves. If you want the number of combinations of 2 gloves you can make from these 10 then you evaluate \$\displaystyle \displaystyle {10\choose{2}}\$.

But since you want the number of combinations without matching pairs, you need to realise that there are 5 matching pairs, so the number of non-matching pairs are

\$\displaystyle \displaystyle {10\choose{2}} - 5\$.
• Feb 16th 2011, 06:13 PM
smallfry
The question says that we choose 4 gloves from 10 though.

Total ways of choosing 4 from 10:
\$\displaystyle \displaystyle {10\choose{4}} = 210\$

Number of ways of choosing TWO pairs of gloves (we don't want this):
\$\displaystyle \displaystyle {5\choose{2}} = 10\$

Number of ways of choosing ONE pair of gloves (we don't want this either):
\$\displaystyle \displaystyle {5\choose{1}}\$ * \$\displaystyle \displaystyle {4\choose{2}}\$ * 2^2 = 130

Total ways = 210 - 10 - 130 = 80
• Feb 16th 2011, 06:22 PM
Prove It
Quote:

Originally Posted by smallfry
The question says that we choose 4 gloves from 10 though.

Total ways of choosing 4 from 10:
\$\displaystyle \displaystyle {10\choose{4}} = 210\$

Number of ways of choosing TWO pairs of gloves (we don't want this):
\$\displaystyle \displaystyle {5\choose{2}} = 10\$

Number of ways of choosing ONE pair of gloves (we don't want this either):
\$\displaystyle \displaystyle {5\choose{1}}\$ * \$\displaystyle \displaystyle {4\choose{2}}\$ * 2^2 = 130

Total ways = 210 - 10 - 130 = 80