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If  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 the value of  is


Question ID - 153649 :-

If  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 the value of  is

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Answer Key : (7) -

(7)

denotes the number of times he can take unit step and  denotes the number of times he can take 2 steps, then ,

Then we must have

If , the steps will be 1 2 2 2

 number of ways

If , the steps will be 1 1 1 22

 number of ways

If , the steps will be 111112

number of ways

If , the steps will be 1 1 1 1 1 1 1

Hence total number of ways



Next Question :

Let  denotes the number of ways in which three people can be selected out of  people sitting in a row, if no two of them are consecutive. If,  then the value of  is


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