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4 quarters are identical and 3 dimes are identical
4 quarters and 3 dimes can be placed in (4 + 3) ! / ( 4! * 3 !) ways = 35 ways

Consider extreme 2 corners are 2 dimes. Then the remaining coins are 4 quarters and 1 dimes.
4 quarters and 1 dime can be arranged in (4 + 1) ! / ( 4! * 1 !) = 5

So the probability is = (Possible 5 cases) / (total cases 35) = 1/7