posted by .

a rabbit can climb one or two steps at a time on a ten step staircase, but he never goes back down. In how many different ways can the rabbit climb a flight of ten steps

5 2's -- one way
4 2's 2 1's ---- number of ways = 6!/(4!2!) = 15
(e.g. 222211, 11222, 212122, etc )

3 2's 4 1's ---- number of ways = 7!/(4!3!) = 35
2 2's 6 1's ---- number of ways = 8!/(2!6!) = 28
1 2 8 1's ---- number of ways = 9!/(1!8!) = 9
all 1's ---- one way

total 1+15+35+28+9+1 = 89

89

I'm lost... what does 7i(backwords)(4i3i) means?
What does the i facing down stands for?

## Similar Questions

Laura is training her pet white rabbit, Sugar, to climb up a flight of 25 steps. Sugar can hop up one or two steps at a time. She never hops back down, only up. How many different ways can Sugar hop up the flight of steps?
2. ### math

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?
3. ### math

An elf has a staircase with 10 steps to climb. Each step it takes can cover either one stair or two stairs. In how many ways can the elf climb the stairs?
4. ### math

An elf has a staircase with 10 steps to climb. Each step it takes can cover either one stair or two stairs. In how many ways can the elf climb the stairs?
5. ### MATH

Adam was walking down the stairs at his work one day. Adam began on the top step and had already gone down seven steps when he saw Reanna on the ground floor beginning to come up the stairs. Reanna goes up two steps for every one step …
6. ### Math

Alice, Beth, and Charlene start climbing a staircase, each with her left foot on step 1 and then her right foot on the next consecutive step. Alice climbs one step at a time, Beth two steps at a time, and Charlene three steps at a …