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
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
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
1,2,3,5,8,13,21,34,55,89
89 is the 10th number
smh
Answered by
Mercedes
32
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