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Question

here is the sol:

in above sol no. of possible 4-pennant is 7 not 5.so it is not the fibonancci series

Comments

its sequence is 1,2,3,7,14,27,55,110,219,439 for coresponding pennant of 1-pennant, 2-pennant,3-pennant........10-pennant respectively

Answer 1

For calculating no of 4 - pennants , we have to take cases :

Case 1 : We have 2 2's :

So in this case no of ways the 2 2's can be permuted = 2! / 2! = 1

Case 2 : We have 4 1's :

So in this case no of ways the 4 1's can be permuted = 4! / 4! = 1

Case 2 : We have 2 1's  and 1  2:

So here we have 3 objects with 1 repetition i.e. corresponding to no of 1's which is 2 in this case.

No of ways if have 2 1's and 1 2 to make sum = 4   :   3! / (2)!   = 3

With this all possibilities are exhausted to get the sum of 4 using 1 and 2 only.

Hence total no of 4 pennants = 1 + 1 + 3  = 5

I suppose u r also taking the pairs (3,1) and (1,3) and that is why u r getting 7 @dileswar sahu.Hope this clears your doubt..

Comments

hmm,exactly i do that........bez of some ques understanding.According to ques only use 1 or 2.