# Combination/ Permutation Question

• May 18th 2010, 11:39 PM
TeriyakiDonnQ
Combination/ Permutation Question
I have a few questions i don't understand T_T

1. A committe of 4 people is to be chosen form a group of 8 people- 4 women and 4 men. How many ways can the committee be chosen so as to include exactly 3 women.

The answer is 70 but i keep getting 96. I don't understand how they got 70 =3=

2. From a deck of 52 cards, the 12 face cards and 4 aces are removed. From the 16 cards, 4 are chosen. How many different ways are there to choose the numbers?

3. In the Lotto 535 lottery, you must choose 4 numbers from 1 to 35 and one number from 1 to 25. How many different ways are there to choose the numbers?

4. Solve for n
nP2= 12
The answer is 4 but i get 5 =3=

n!/ n-2! = 12
then i expanded and canceled out that n! leaving me (n-2)(n-1) = 12
i expanded it then i get n^2- 3n+2 = 12
i got n= 5 and -2
D:
i don't know what i did wrong.

help anyone? (:
• May 19th 2010, 12:16 AM
matheagle
For (1) I get 16 since ${4\choose 3}{4\choose 1}=(4)(4)=16$

(4) IT's n(n-1)=12 producing $n^2-n-12=(n-4)(n+3)=0$ so n=4
• May 19th 2010, 12:17 AM
TeriyakiDonnQ
Quote:

Originally Posted by matheagle
I get 16

Ohh. o_o
weird T_T
i don't like these questions
• May 19th 2010, 12:22 AM
matheagle
so how did you get 96 and who says its 70?
• May 19th 2010, 12:32 AM
TeriyakiDonnQ
Quote:

Originally Posted by matheagle
so how did you get 96 and who says its 70?

O; oh em gee. nvm it's 16 D:
i was looking at another question =3=

buut. i think using the 8 instead the 4 thats why i was getting such big numbers.
but how do you know it's a combination or a permutation from

( 4 3 ) (4 1)
• May 19th 2010, 12:32 AM
downthesun01
I thought it was 16 too.

${8\choose 4}=70$, which would be the number of ways to select 4 people out of 8 disregarding gender. Maybe you're reading the wrong answer?

Haha.. you just beat me to it.

It's a combination, because the order doesn't matter.
• May 19th 2010, 12:36 AM
matheagle
you want to pick 3 women from a group of 4.

that's ${4\choose 3}=4$

you can write out ABCD women, and see there are 4 ways.
BUT the easier way is to cast off one and see there are 4 cast offs, leaving you with 3 women
ABC sending D home alone
ABD sending off C
ACD sending off B
BCD sending off A

same with 1 man from 4, there are 4 men to choose from.
• May 19th 2010, 12:40 AM
TeriyakiDonnQ
Quote:

Originally Posted by matheagle
you want to pick 3 women from a group of 4.

that's ${4\choose 3}=4$

you can write out ABCD women, and see there are 4 ways.
BUT the easier way is to cast off one and see there are 4 cast offs, leaving you with 3 women
ABC sending D home alone
ABD sending off C
ACD sending off B
BCD sending off A

same with 1 man from 4, there are 4 men to choose from.

okkay. i think i got it xP
• May 19th 2010, 12:48 AM
downthesun01
2. It looks like their just asking for the number of ways to choose 4 cards out of the remaining 16, although I'm not too sure what is meant by "numbers."

Anyway, ${16 \choose 4} =...$

3. It's the number of ways to choose 4 numbers out of 35 multiplied by the number of ways to choose 1 number out of 25
• May 19th 2010, 12:54 AM
TeriyakiDonnQ
Quote:

Originally Posted by downthesun01
2. It looks like their just asking for the number of ways to choose 4 cards out of the remaining 16, although I'm not too sure what is meant by "numbers."

Anyway, ${16 \choose 4} =...$

okay...