Amy can travel clockwise or anticlockwise on the diagram.

Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.

Similarly, anticlockwise she has four different routes.

Total routes = 8

B is the son of C but C is not the mother of B means C is the father of B A is marned to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C 

E is the brother of C who is the father of D. So. E is the uncle of D. 

B is the son of C but C is not the mother of B means C is the father of B A is marned to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C.

Clearly, the females are only the mother A and the daughter D 

B is the son of C but C is not the mother of B means C is the father of B A is marned to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C

A has son B, son F and daughter D it three children. 

B is the son of C but C is not the mother of B means C is the father of B. A is marned to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C

Clearly. A is the mother of B. 

B is the son of C but C is not the mother of B means C is the father of B. A is marned to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C

A is the mother and hence female. B is the son and hence male. C is the husband and hence male.

D in the daughter and hence female. E is the brother and hence male F is the son and hence male.

So, there are four males. 

He can arrange his schedule in 8P6 = 20160 ways

The smallest number in the series is 1000, a 4-digit number.

The largest number in the series is 4000, the only 4-digit number to start with 4. 

The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.

Including 4000, there will be 376 such numbers.