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?

Answer 1

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

Answer 2

32 times

Answer 3

89

Answer 4

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

Answer 5

use fibbonacchi sequence idiots
1,2,3,5,8,13,21,34,55,89
89 is the 10th number
smh

Answer 6

32