Permutations Quiz

[zelwin]

Hi Everyone,

I'm new to the Forum so I thought I'd introduce myself wilh a little brain teaser.


OK, so,
you have 4 checkboxes,
each has 2 values, (1,0)
Only 1 value can be selected at a time (per checkbox)

How many Possible permutations of checkboxes are there ?

[Glaysher]

0,0,0,0 gives 1 possible
1,0,0,0 gives 4 possibles
1,1,0,0 gives 3 + 2 + 1 = 6 possibles
1,1,1,0 gives 4 possibles
1,1,1,1 gives 1 possible

1 + 4 + 6 + 4 + 1 = 16 possibles

[Prodian]

Hi Everyone,

I'm new to the Forum so I thought I'd introduce myself wilh a little brain teaser.


OK, so,
you have 4 checkboxes,
each has 2 values, (1,0)
Only 1 value can be selected at a time (per checkbox)

How many Possible permutations of checkboxes are there ?

Been along time since i've done permutations but... uh...
Each checkbox has 2 values so the total combinations for 1 checkbox is 2.
There are 4 checkbox so it would be 2^4. I think.
That gives you 16 combinations. I may be wrong.

Someone beat me to it Oh well. At least it looks like I was right.

[zelwin]

0,0,0,0 gives 1 possible
1,0,0,0 gives 4 possibles
1,1,0,0 gives 3 + 2 + 1 = 6 possibles
1,1,1,0 gives 4 possibles
1,1,1,1 gives 1 possible

1 + 4 + 6 + 4 + 1 = 16 possibles

I think you are on the right track but there is a third dimension,

1,0,0,0
1,1,0,0
1,1,1,0
1,1,1,1

0,1,0,0
0,1,1,0
0,1,1,1

0,0,1,0
0,0,1,1
0,0,0,1


ETC...

[zelwin]

I think you are on the right track but there is a third dimension,

1,0,0,0
1,1,0,0
1,1,1,0
1,1,1,1

0,1,0,0
0,1,1,0
0,1,1,1

0,0,1,0
0,0,1,1
0,0,0,1


ETC... I may be very wrong though.

This problem refers to 4 check boxes that i have to state wether an item has, or has not, got one of these features

yes=1
no=0

The items can have any combination of features. I am not so good at maths and having looked up how to calculate Permutations i was completely confused so i tried to work it out on paper.

Origionally i came up with 13 but then notised i had missed out 2 possible combinations so i now have 15

If you are right with 16 then I am pretty happy and very thankfull as it means i have only missed 1.

[Glaysher]

I think you are on the right track but there is a third dimension,

1,0,0,0
1,1,0,0
1,1,1,0
1,1,1,1

0,1,0,0
0,1,1,0
0,1,1,1

0,0,1,0
0,0,1,1
0,0,0,1


ETC...

I have counted all those. I just didn't write out the different orders, just how many different orders exist for each possible combination of 0s and 1s

[Glaysher]

All possible

0,0,0,0
1,0,0,0
0,1,0,0
0,0,1,0
0,0,0,1
1,1,0,0
1,0,1,0
1,0,0,1
0,1,1,0
0,1,0,1
0,0,1,1
1,1,1,0
1,1,0,1
1,0,1,1
0,1,1,1
1,1,1,1

[krtxmrtz]

you have 4 checkboxes,
each has 2 values, (1,0)
Only 1 value can be selected at a time (per checkbox)

How many Possible permutations of checkboxes are there ?

This is the same as generating all possible binary numbers with four digits, so 2⁴.

[zaza]

Incidentally, be careful when using the word "permutations". This often implies that things can be swapped around, so 1,2 is different from 2,1. In your case, you are really looking for the number of combinations of these checkboxes.

4C0 + 4C1 + 4C2 + 4C3 + 4C4

=

1 + 4 + 6 + 4 + 1

=

16 as stated above.

[zelwin]

Thank you all very much

[Glaysher]

You're welcome