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If N is the number of ways in which a person can walk up a sta

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If $N$ is the number of ways in which a person can walk up a stairway which has $7$ steps if he can take $1$ or $2$ steps up the stairs at a time, then find the value of $\frac{N}{3}$ .

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N

is the number of ways in which a person can walk up a stairway which has

7

steps if he can take

1

2

steps up the stairs at a time, then find the value of

\frac{N}{3}

10 mins ago

Discuss this question LIVE

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Text solutionVerified

x

denotes the number of times he can take unit step and

y

denotes the number of times he can take

2

steps, then

x + 2 y = 7

Then we must have

x = 1, 3, 5

x = 1

, the steps will be

1222

\Rightarrow

number of ways

= \frac{4 !}{3 !} = 4

x = 3

, the steps will be

11122

\Rightarrow

number of ways

= \frac{5 !}{2 ! .3 !} = 10

x = 5

, the steps will be

111112

\Rightarrow

number of ways

=^{6} C_{1} = 6

x = 7

, the steps will be

1111111

\Rightarrow^{7} C_{0} = 1

Hence total number of ways

= N = 21

\Rightarrow \frac{N}{3} = 7

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Question Text	If $N$ is the number of ways in which a person can walk up a stairway which has $7$ steps if he can take $1$ or $2$ steps up the stairs at a time, then find the value of $\frac{N}{3}$ .
Answer Type	Text solution:1
Upvotes	150