There are two outcomes to each event: the solution is 2^7. there. figure that out, i dont have my calculator on me.
i live on the first floor of my building. everyday we come back after a walk me and my dog need to climb 7 stairs. forget about me, how many ways can my dog climb them if he climbs 1-2 stairs in one step.
eg. he may either climb the 7 stairs by climbing 2, then 2, then 2, then 1, or 1, then 2, then 2, then 2, or he may climb then as 2,2,1,1,1........in total, how may possible ways? thats all i mean.
This is not correct (and you need a calculator? 2^7 = 2^3 x 2^3 x 2 = 8 x 8 x 2 = 64 x 2 = 128)
The possible combinations are:
(2, 2, 2, 1)
(2, 2, 1, 1, 1)
(2, 1, 1, 1, 1, 1)
(1, 1, 1, 1, 1, 1, 1)
You have to calculate the number of distinct arrangements of each combination and add them together:
There are two ways in which one can reach the stair(to be done in ways).
One way is that one reaches the stair which can be done in ways and then reach the stair by climbing steps in one go.
Second way is that one reaches the stair which can be done in ways and then reach the stair by climbing the remaining stair.
Therefore,