Asked by kC

a rabbit climb up a flight of 10 stairs and can only hop 1 or 2 steps each time. he never hops down, only up. How many ways can the rabbit hop up the flight of 10 steps?

Answers

Answered by Reiny
First lets look at the number of combinations (order won't matter) to go the 10 steps
Behind it I will then do the number of permutations

2 2 2 2 2 ---- 1
2 2 2 2 1 1 --- 6!/(4!2!) = 15
2 2 2 1 1 1 1 --- 7!/(3!4!) = 35
2 2 1 1 1 1 1 1 --- 8!/(2!6!) = 28
2 1 1 1 1 1 1 1 1 --- 9!/(1!8!) = 9
1 1 1 1 1 1 1 1 1 1 --- 1

total = 1+15+35+28+9+1 = 89
Answered by jack
32 times
Answered by Jeff
89
Answered by EDUARDO
Combination
Number of ways
ten 1's
1
eight 1's, one 2
(
9
8
,
1
)
=
9
six 1's, two 2's
(
8
6
,
2
)
=
28
four 1's, three 2's
(
7
4
,
3
)
=
35
two 1's, four 2's
(
6
2
,
4
)
=
15
five 2's
1



Therefore, there are:
1
+
9
+
28
+
35
+
15
+
1
=
89
ways
Answered by Rishard
use fibbonacchi sequence idiots
1,2,3,5,8,13,21,34,55,89
89 is the 10th number
smh
Answered by Mercedes
32
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