Possible Arrangements: A family has three children....

S

shay

New member
Joined
Jun 16, 2006
Messages
4
A family has three children. I am to write down all the possible arrangements for three children oldest to youngest.

Do I have all of the possible arrangements B= boy G= girl; in order from oldest to youngest

bgb
bbg
gbb
gbg
ggb
bgg
bbb
ggg
 
Yes you do. But it is better to be systemic about it.
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG.

Look up how one makes a ‘TRUTH TABLE’.
Then use B & G instead of T & F.
You can also use this for coin tossing using T & H.
 
Re: Possible Arrangements

shay said:
A family has three children. I am to write down all the possible arrangements for three children oldest to youngest.
Click to expand...
What's "oldest to youngest" got to do with this?
 
Re: Possible Arrangements

Denis said:
What's "oldest to youngest" got to do with this?
Click to expand...
If there are two girls and one boy, there are three different arrangement possible, depending upon whether the boy is the eldest, the middle, or the youngest child.

Eliz.
 
Hello, shay!

pka is absolutely correct . . . you need a system.

There are two possible "values": \(\displaystyle \,\{B,G\}\)

If there are \(\displaystyle n\) children, there are \(\displaystyle 2^n\) possible outcomes.


So with 3 children, there are \(\displaystyle 2^3\,=\,8\) outcomes.

We will make a 3-column table.

In column-1, write B's and G's four-at-a-time: \(\displaystyle \;\begin{array}{cccccccc}B\\B\\B\\B\\G\\G\\G\\G\end{array}\)

In column-2, write B's and G's two-at-a-time: \(\displaystyle \;\begin{array}{cccccccc}B\\B\\G\\G\\B\\B\\G\\G\end{array}\)

In column-3, write B's and G's one-at-a-time: \(\displaystyle \;\begin{array}{cccccccc}B\\G\\B\\G\\B\\G\\B\\G\end{array}\)


Reading across the table, we have all eight possible outcomes:

\(\displaystyle \;\;\;\begin{array}{cccccccc}1&B&B&B\\2&B&B&G\\3&B&G&B\\4&B&G&G\\5&G&B&B\\6&G&B&G\\7&G&G&B\\8&G&G&G\end{array}\)

 
You must log in or register to reply here.
Top