# math

posted by .

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?

• math -

5 Doubles === 1 way
4 Doubles, 2 Singles === e.g. DDSSDD
number of ways = 6!/(2!4!) or C(6,4) = 15
3 Doubles, 4 Singles === C(7,3) = 35
2 Doubles , 6 Singles === C(8,2) = 28
1 Double , 8 Singles === C(9,1) = 9
10 Singles === 1

total = 89

• math -

...what?

• math -

i don't understand how its 89 ways!
how about 20 stairs, and N stairs? what would be the equation for that?

## Similar Questions

1. ### math

ol' santas pack held thirty toys made by his elfin crew; and though none made the same amount, each elf made more than two. the elf named cher made one more toy than the elf who dressed in reds, but cher made one less christmas toy …
2. ### physics

A golf bounces down a flight of steel stairs, striking several steps on the way down, but never hitting the edge of a step. The ball starts at the top step with a vertical velocity component of zero. If all the collisions with the …
3. ### 8th grade

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
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 …
7. ### math

How many different ways can an elf climb a ten-step staircase if he or she climbs only one of two steps a time?
8. ### chemistry

49-kg woman cheats on her diet and eats a 582-Calorie (582 kcal) jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut?
9. ### physics

calculate the number of kilocalories needed to climb 232 stair steps (116 steps per minute for 2 min.) climbing stairs (116/min.) = energy consumption rate is 9.8 (kcal/min)
10. ### Physics

Two men of the same mass climb the same flight of stairs. The first man climbs the stairs for 25 seconds, while the seconds person takes 35 seconds. Which man does the most work?

More Similar Questions