Perms/Combs Quick Questions (1 Viewer)

[GaDaMIt]

just revising for my preliminary yearly and either i dont understand, or am getting slightly different answers

1) 6 people sitting at a table, Find how many ways this can be done if Rosy sits on Jilian's left hand side?

Im thinking a hexagons vertices, so there would only be 2 places that could be considered left of Jilian.. leaving 4 seats left over

2 x 4!

= 48, but answer is 120


2) A committee of 3 is to be chosen from 3 boys and 4 girls

How many committees are possible if a particular boy is to be on the committee

im thinking 1C1 x 6C2 = 15 which is the correct answer, but this doesn't take into consideration the possibility that the person chosen is a girl???


3) A team of 10 boys and 10 girls prefects is to be chosen from a group of 21 boys and 19 girls

If Katrina and John are hoping to be chosen, find the probability that
a) both will be chosen
b) only one will be chosen


4) Made this one up myself, not sure on how to approach a question where you have to use less letters than given, but some may be the same

How many 3 letter words can be made from the word BOOK? If this has some sort of exception due to short amounts of EDIT LETTERS /EDIT making it easier, the same question for the word ABCCDDDEFGGH?

 

[sweet fairy]

hey second time post, first time helper. Just did my ext math yearly hard as!!

1) 6 people sitting at a table, Find how many ways this can be done if Rosy sits on Jilian's left hand side?

well you know round table questions means the placement of the first person is arbitrary (there 'stuck' and everyone around them are the people who move).

Therefore with no restrictions the anwer for total permuation is 5!
Normally when 2 people have to sit together they can sit in 2! ways eg either AB or BA
Without resitrictions the total combinations would be 2! x 5!

However Rosy has to sit on Jullians left side.
Therefore they can only sit in the AB position (it doesn't matter which is lef tor right as they are fixed)

therefore the answer is 5! = 120.


2) A committee of 3 is to be chosen from 3 boys and 4 girls

How many committees are possible if a particular boy is to be on the committee

sorry you're wrong

the total committee would be 7C3

however one boy has to be in this leaves 6 other people (boy or girl) to fill the spot, and only 2 spaces left since that boy always has to be in.

so the answer is 6C2

3) A team of 10 boys and 10 girls prefects is to be chosen from a group of 21 boys and 19 girls

If Katrina and John are hoping to be chosen, find the probability that
a) both will be chosen
b) only one will be chosen

total combinations = 21C10 x 19C10

a) both chosen
if john must be chosen then
20C9
if kat must be chosen
18C9
the combination for that is: 20C9 x 18C9

the probability is the desired outcome / total possible outcomes
(20C9 x 18C9) / 21C10 x 19C10.

b) for this one find the combinations if john get chosen without kat, then find the combinations of kat getting chosen without john, add them together and divde by the total combinations. I think. It might be that you don't have to add them together? Never had a question like this b4.




good luck i hope this help.

 

[Riviet]

How many 3 letter words can be made from the word BOOK?

You have an identical set of letters so you need to consider cases.

Case 1: word contains 2 O's
O_O

OO_

_OO

Therefore 3 ways to arrange O's OR 3C2 ways. For remaining spot, there are 2 letters left to fill in so 2C1 ways.
.'. 3 x 2 = 6 ways

Case 2: word contains 1 O:
_ _ O
_O_
O _ _ => 3 ways to place O

We can't choose the other O as we can only have 1 O for this case so we have to choose the remaining two letters. They can be placed in the remaining two spots in 2! ways.
.'. 3 x 2 = 6 ways
You can't have a three letter word with no O's in this example, having only 2 other letters other than the O's.
Therefore the total number of ways is 6+6=12 ways.