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8!/2! as (d,b) is the only permitted arrangement between d and b , so it is equivalent to treating them as similar objects.
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If d is at position 1, then total permutations = 7!

if d is at position 2 = choices for placing b * permutation of remaining objects = 6 * 6!

if d is at position 3 = 5 * 6!

similarily, for pos = 4, total permutations = 4 * 6!

for pos = 5, total permutations = 3 * 6!

for pos = 6, total permutations = 2 * 6!

for pos = 7, total permutations = 1 * 6!

=> total permutations  = 6!(7 + 6 + 5 + 4 + 3 + 2 + 1) = 6! * 28

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