# Thread: Past exam questions help

1. ## 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

2. 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)

Thanks!
Too many questions in one thread.

3. 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.

4. 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 $\displaystyle {10\choose{2}}$.

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

$\displaystyle {10\choose{2}} - 5$.

5. The question says that we choose 4 gloves from 10 though.

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

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

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

Total ways = 210 - 10 - 130 = 80

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

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

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

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

Total ways = 210 - 10 - 130 = 80