Let b1b2b3b4 be a 4-element permutation with bi $\in$ {1, 2, 3, ........, 100} for 1 $\le$ i $\le$ 4 and bi $\ne$ bj for i $\ne$ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1b2b3b4 is equal to ____________.

Question

Let b₁b₂b₃b₄ be a 4-element permutation with b_i $\in$ {1, 2, 3, ........, 100} for 1 $\le$ i $\le$ 4 and b_i $\ne$ b_j for i $\ne$ j, such that either b₁, b₂, b₃ are consecutive integers or b₂, b₃, b₄ are consecutive integers. Then the number of such permutations b₁b₂b₃b₄ is equal to ____________.

Correct Answer

18915

Solution

Please login to view the detailed solution steps...

Go to DASH