p&c q14

[pka]

In how many ways can a 12 step staircase be climbed taking 1 step or 2steps at a time ?

You really ought to start a new tread with any new question.
Using only single steps there is only one way to reach the twelfth step.
Using only six double steps there is only one way to reach the twelfth step.
Now Using six single steps and three double steps how many ways are there to reach the twelfth step?
HINT: How many ways can one rearrange the string [imath]SSSSSSDDD~?[/imath]

 

[Dr.Peterson]

You are intelligent enough to catch me .
I gave up and saw solution understood it , then wrote without seeing.

And I assumed you were honest.

In how many ways can a 12 step staircase be climbed taking 1 step or 2steps at a time ?


Now the approach is
Either 12 single steps --> 12c1=12 .

Or
10 single steps and one two Steps= 12c2= 66

Total 78

where am I wrong?

I will not respond to this until you put it in a new thread. It is entirely unrelated to this one. The standard solution to this doesn't even use combinations or permutations, though it can be done that way.

 

[Saumyojit]

three double steps

in the question 2 steps at a time means at one moment he can take two step at a time but that doesn't mean he can take only one two steps in the entire journey at a time .

 

[pka]

in the question 2 steps at a time means at one moment he can take two step at a time but that doesn't mean he can take only one two steps in the entire journey at a time .

Comment: This is such a standard counting problem that there is no need to tell either of us the workings of it.
There are eleven ways to reach the twelfth step using one twostep and ten single steps.
That is the number of ways that one can rearrange the string [imath]EEEEEDEEEEE[/imath]

 

[Saumyojit]

Comment: This is such a standard counting problem that there is no need to tell either of us the workings of it.
There are eleven ways to reach the twelfth step using one twostep and ten single steps.
That is the number of ways that one can rearrange the string [imath]EEEEEDEEEEE[/imath]

please discuss it in my recnet thread