Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

A man climbs either one step or k steps at a time. Let A(1,k) be the number of ways he can climb a staircase of 3k steps from the bottom, where k is at least 2.

If $A (1, k + 1) - A (1, k) = λ_{k}$ , find $λ_{k + 1} - λ_{k}$ .

Options:

Answer:

Solution:

From the expression for $A (1, k)$ , simplification gives $λ_{k} = k + 4$ . Hence $λ_{k + 1} - λ_{k} = 1$ .

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: QB

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