Others Maths Puzzle

Find the remainder when 4^5^6^7 + 1 is divided by 10?

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Others Other Question

In how many way can 210 be expressed as a product of 3 distinct factors?
My answer is 16(4c2+4c2+4c3),but the actual ans is 13...pls give me a plausible solution! The set Y={3,3^(1/2),3,3^(3/2),,,,3^9,3^(19/2),3^10}
in how many ways can a pair of distinct numbers can be selected from the set such that their product is greater than or equal to 3^10 ?