Every 4-permutation consisting of 4 consecutive numbers. in order, has been double counted.
Examples of 4-permutations consisting of 4 consecutive numbers. in order:
{1, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}, .... , {97, 98, 99, 100}.
How they have been double counted?
suppose a 4 permutation {2, 3, 4, 5}
Once we counted it while counting all the permutations of type {2, 3, 4, x} where x can be any element of the set {1, 5, 6, 7, ... ,99 , 100}, when x = 5,
Second time we counted it while counting all the permutations of type {y, 3, 4, 5} where y can be any element of the set {1, 2, 6, ... ,99 , 100},when y = 2.
Thus we counted {2, 3, 4, 5} twice(although in different manners).
Similarly for each of the 97, four permutations consisting of 4 consecutive numbers.