Consider the set S = {(a, b, c, d, e): 0 < $a$ < $b$ < $c$ < $d$ < e < 100} where a, b, c, d, e are integers. If D is the average value of the fourth element of such $a$ tuple in the set, taken over all the elements of S, find the largest integer less than or equal to D.

Step 1: d = 4 sum = 4 × 95C1 × 3C3

Step 2: d=5 sum = 5 × 94C1 × 4C3

Step 3: d=6 sum = 6 × 93C1 × 5C3

Step 4: d = 98 sum = 98 × nC1 × 97C3

Step 5: Total = 4  95C1  3C3 + 5  94C1  4C3 … × 98 1C1  97C3

Step 6: (99 − $r$ ) 98−r

Step 7: = 4 .r C3

Step 8: = 4  99−r C4 \times r

Step 9: = 4 \times 100C6

Step 10: 4 \times 100C6

Step 11: => A.M =

Step 12: =>  3  = 66