Let b 1 b 2 b 3 b 4 be a 4-element permutation with b i 
{1, 2, 3, ........., 100} for 1 
i 
4 and 
for 
, such that either b 1 , b 2 , b 3 are consecutive integers or b 2 , b 3 , b 4 are consecutive integers.Then the number of such permutations b 1 b 2 b 3 b 4 is equal to________.
Text Solution
Verified by Experts18915
(18915)
b i 
{1,2,3.........100}
Let A = set when b 1 b 2 b 3 are consecutive
Similarly when b 2 b 3 b 4 are consecutive
N(a) = 97 x 98
Similarly when b 2 b 3 b 4 are consecutive
n(b) = 97 x 98
n(A 
B) = 97
n(A 
B) = n(a)+n(b) - n(A 
B)
Number of permutation = 18915
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