Permutations and Combinations (1 Viewer)

Sparklingstar

New Member
Joined
Sep 28, 2011
Messages
6
Gender
Female
HSC
2013
Hi :jump:,
Can someone please help me with this question?

A girl has 6 pairs of earrings, 3 t-shirts, 2 pairs of jeans and 8 pairs of shoes. If she wishes to choose one of each article, how many ways can she dress up to go out?
The answer is 288

Thankyou :)
 

enoilgam

Moderator
Moderator
Joined
Feb 11, 2011
Messages
11,876
Location
Mare Crisium
Gender
Undisclosed
HSC
2010
*Moved to Maths Extension 1 Forum*

This may sound stupid (I dont know if it is correct), but wouldnt you do 3x2x8x6 = 288, because there are no restrictions on the combinations. I'm not sure at all though.
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
*Moved to Maths Extension 1 Forum*

This may sound stupid (I dont know if it is correct), but wouldnt you do 3x2x8x6 = 288, because there are no restrictions on the combinations. I'm not sure at all though.
Still got it in you I see :p
 

Shadowdude

Cult of Personality
Joined
Sep 19, 2009
Messages
12,146
Gender
Male
HSC
2010
*Moved to Maths Extension 1 Forum*

This may sound stupid (I dont know if it is correct), but wouldnt you do 3x2x8x6 = 288, because there are no restrictions on the combinations. I'm not sure at all though.
That's right.


A girl has 6 pairs of earrings, 3 t-shirts, 2 pairs of jeans and 8 pairs of shoes. If she wishes to choose one of each article, how many ways can she dress up to go out?

1. Choose a pair of earrings... 6 ways
2. Choose one T-shirt... 3 ways
3. Choose a pair of jeans... 2 ways
4. Choose one pair of shoes... 8 ways

Answer: 6*3*2*8 = 288


Yet again, pro-tip: set out your working clearly.
 

Sparklingstar

New Member
Joined
Sep 28, 2011
Messages
6
Gender
Female
HSC
2013
How about this question?

A family consists of a father, a mother, 3 girls and 4 boys.
If the same family is seated randomly at a round table, find the probability that the parents are separated by exactly two seats, and these seats are both occupied by boys?

Thanks:)
 
Last edited:

Shadowdude

Cult of Personality
Joined
Sep 19, 2009
Messages
12,146
Gender
Male
HSC
2010
How about this question?

A family consists of a father, a mother, 3 girls and 4 boys.
If the same family is seated randomly at a round table, find the probability that the parents are separated by exactly two seats, and these seats are both occupied by boys?

Thanks:)
This is a 'successes' / total possibilities probability question.

Total possibilities to seat nine people on the round table: 8!

A 'success' is when the parents are separated by two seats AND these seats in between are both occupied by boys

1. Seat a parent at the table... 2 ways
2. Choose 2 boys to seat next to the first parent... C(4,2) ways
3. Arrange these boys in the two seats... 2! ways
4. Seat the other parent next to these two boys... 1 way
5. We have three girls and two boys remaining, arrange them in the remaining 5 chairs... 5! ways

Answer: 2*C(4,2)*2!*1*5! / 8!

= 1/14.


In the words of Rainbow Dash: OHHHHHHHH YEEAH
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top