There are 8 steps on a flight of steps leading from one level to another. A person can take at most 3 steps at a time. In how many ways on the person reach
the upper level from the lower one?
O 64
0 81
O 100
128
Answers
Given : There are 8 steps on a flight of steps leading from one level to another. A person can take at most 3 steps at a time
To Find : In how many ways on the person reach the upper level from the lower one
64
81
100
128
Solution:
Person can take 3 steps maximum 2 times
3 x 2 + 2 = 8 ways = ³C₂ = 3
3 x 2 + 1 + 1 = 8 Ways = ⁴C₂ = 6
Person take 3 steps once
3 x 1 + 2 x 2 + 1 = 8 ways = ⁴C₁. ³C₂ = 12
3 x 1 + 2 x 1 + 1 x 3 = 8 ways = ⁵C₁. ⁴C₁ = 20
3 x 1 + 1 x 5 = 8 ways = ⁶C₁ = 6 ways
Person Does not take 3 steps
2 x 4 = 8 ways = 1
2 x 3 + 1 x 2 = 8 ways = ⁵C₃ = 10
2 x 2 + 1 x 4 = 8 ways = ⁶C₂ = 15
2 x 1 + 1 x 6 = 8 ways = ⁷C₁ = 7
Person takes single steps only
1 x 8 = 8 ways = 1
3 + 6 + 12 + 20 + 6 + 1 + 10 + 15 + 7 + 1
= 81
81 Ways
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