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Hi,

I have some queries that I'm hoping you can help me with. Actually these are probably fairly straight forward for this forum but it's been a long time since I've done any formal math so some help would be appreciated.

First query: suppose I have 4 objects: A, B, C and D. I want to know how many possible combinations there are that I can arrange them into, e.g. ABCD, ABDC, DACB etc etc.

If I've remembered this correctly, this is a problem that can be solved using a factorial function? I.e. there are 4 objects, so the total number of possible combinations that they can be arranged in is 4! = 4 x 3 x 2 x 1 = 24.

I think this is right but can someone confirm?

Secondly, suppose I have the same 4 objects and I can assign them a value of either 1 or 0, making them variables with two possible states. I need to know the formula for working out how many possible combinations of states there are. I have done this manually by simply creating a table/matrix and have come up with an answer of 15 different possible states but I don't know the formula for working it out, it was just trial and error and 15 seems a bit of an odd number, personally I would have thought 16 (4^2) would make more sense but I cannot find any other combination other than the 15 I've already got.

ABCD

1000

0100

0010

0001

1100

1010

1001

0110

0101

0011

1110

1101

1011

0111

1111

However this method is a total ball-ache, even with just 4 numbers so it would obviously be much easier if I could just apply a formula. Note that in this case I don't want to change the ABCD order, just the value of each variable, 1 or 0, and then to know how many different combinations of states there are altogether.

Thanks in advance for any help.

-Rob

I have some queries that I'm hoping you can help me with. Actually these are probably fairly straight forward for this forum but it's been a long time since I've done any formal math so some help would be appreciated.

First query: suppose I have 4 objects: A, B, C and D. I want to know how many possible combinations there are that I can arrange them into, e.g. ABCD, ABDC, DACB etc etc.

If I've remembered this correctly, this is a problem that can be solved using a factorial function? I.e. there are 4 objects, so the total number of possible combinations that they can be arranged in is 4! = 4 x 3 x 2 x 1 = 24.

I think this is right but can someone confirm?

Secondly, suppose I have the same 4 objects and I can assign them a value of either 1 or 0, making them variables with two possible states. I need to know the formula for working out how many possible combinations of states there are. I have done this manually by simply creating a table/matrix and have come up with an answer of 15 different possible states but I don't know the formula for working it out, it was just trial and error and 15 seems a bit of an odd number, personally I would have thought 16 (4^2) would make more sense but I cannot find any other combination other than the 15 I've already got.

ABCD

1000

0100

0010

0001

1100

1010

1001

0110

0101

0011

1110

1101

1011

0111

1111

However this method is a total ball-ache, even with just 4 numbers so it would obviously be much easier if I could just apply a formula. Note that in this case I don't want to change the ABCD order, just the value of each variable, 1 or 0, and then to know how many different combinations of states there are altogether.

Thanks in advance for any help.

-Rob

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