Question
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
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
jack
32 times
Jeff
89
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
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
Mercedes
32