How many permutations

Loki123 said:
Any advice? I don't know how to do this View attachment 32597
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I think you have a good idea to start; but I can't be sure, because you haven't told us what you are thinking in words. Once you tell us your thinking, we should be able to help you with the next step.

It looks like you are arranging the other 9 numbers, and then thinking about how many places the 0 and 1 can be inserted. But what does 11-4=7 have to do with your thinking? This step should not be hard, once you think clearly about it. (You could just count in your picture.)
 
Dr.Peterson said:
I think you have a good idea to start; but I can't be sure, because you haven't told us what you are thinking in words. Once you tell us your thinking, we should be able to help you with the next step.

It looks like you are arranging the other 9 numbers, and then thinking about how many places the 0 and 1 can be inserted. But what does 11-4=7 have to do with your thinking? This step should not be hard, once you think clearly about it. (You could just count in your picture.)
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i would assume 9! * 10 but it's 9! * 16, which i don't get how they got. 11-4=7 is just an idea that i discarded
 
[imath]\dbinom{9}{2}=36[/imath] ways to select exactly two other numbers to be between [imath]0~\&~1[/imath].
Lets build a block of those four numbers. That block looks like [imath]\boxed{0XY1}\text{ or }\boxed{1XY0}[/imath]
How many such blocks are there?
Each block can be arranged with the other seven in [imath]8![/imath] ways.
What is the answer?
 
pka said:
[imath]\dbinom{9}{2}=36[/imath] ways to select exactly two other numbers to be between [imath]0~\&~1[/imath].
Lets build a block of those four numbers. That block looks like [imath]\boxed{0XY1}\text{ or }\boxed{1XY0}[/imath]
How many such blocks are there?
Each block can be arranged with the other seven in [imath]8![/imath] ways.
What is the answer?
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9! * 16
 
Loki123 said:
i put lines where i think the four 1aa0 could go. 10 places in total
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Why do you say ten places? there are eleven members in [imath]\{0,1,2,3,4,5,6, 7, 8, 9,10\}[/imath]
I get [imath]144[/imath] passible blocks: [imath]\boxed{0XY1}[/imath] The X can have nine values, the Y can have eight.
The block [imath]\boxed{0691}[/imath] can be arranged in four ways: [imath]\boxed{0691}\boxed{1960}\boxed{0961}\boxed{1690}[/imath]
How do we put these together?
 
Loki123 said:
i put lines where i think the four 1aa0 could go. 10 places in total
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1651786849581.png​
If you mean the left end of "1aa0" (or "0aa1") can go, the rightmost 2 don't work.

Or think of it as going in one of these 8 places:

1651787036835.png​

So there are 8 places, and 2 orders, for a total of 9!*8*2.
 
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