JEE Advanced Model Paper 5 with solutions for online practice

Answer (8)
Let the 100 things are A1 , A2 ... A100 fixed on circle.
If A1 is selected then A2 and A100 cannot any twonon - adjacent of A1 he selected from A3 to A99 . This can be done by

97

‌

C2 - 96 = 4560 ways . Similarly for other two letters also .
∴ Total number of selections = 4560 × 100
= 456000 , but here every thing is counted threetimes.
∴ N =

1

3

× 456000 = 125000