Respuesta :
Answer: There are 24 ways.
Step-by-step explanation:
All the numbers are divisible by 11, so divide all the numbers by 11 to make the problem simpler: Jo climbs a flight of 6 stairs. Jo can take the stairs 1, 2, or 3 at a time.
A recursive approach can now solve this problem. The number of ways to climb one stair is 1. There are two ways to climb 2 stairs: (1, 1) or (2). For 3 stairs, there are 4 ways: (1, 1, 1), (1, 2), (2, 1), and (3). Extending this pattern, there are 1+2+4 = 7 ways to climb up 4 stairs, 2+4+7 = 13 ways to climb up 5 stairs, and 4+7+13 = 24 ways to get up 6 stairs.
The total number of ways by which Jo climbs the stairs at school when he can take the stairs 1, 2, or 3 at a time.
What is arrangement?
Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways. The number of possible ways to arrange is n!.
Here, n is the number of objects.
Every day at school, Jo climbs a flight of 6 stairs. Jo can take the stairs 1, 2, or 3 at a time. For example, Jo could climb 3, then 1, then 2.
With one stair, there is one way to climb. With two stairs, the ways to climb are two 1-1 at a time or 2 at a time. For the three stair, there are 4 ways,
[tex]1+1+1,1+2,2+1,3[/tex]
For the three stair, there are 7 possibilities he can climb the stair.
[tex]1+1+1+1,\;1+1+2,\;1+2+1,\;2+2\;,2+1+1\;1+3.\;3+1[/tex]
In the same way for the 5 the stair there are 6 additional steps add in it, which makes it 13.
For the six stair for single step, we have 13 ways, for double step we have 7 ways and for triple step we have 4 ways. Thus,
[tex]\rm Number\; of \; ways=13+7+4\\\rm Number\; of \; ways=24[/tex]
Thus, the total number of ways by which Jo climbs the stairs at school when he can take the stairs 1, 2, or 3 at a time.
Learn more about the arrangement here;
https://brainly.com/question/6032811
