Question

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3

Answer 1

Consider four blanks

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$7$ is in thousand place, then $3$ can be placed in any of the $3$ places in $3$ ways.
Remaining two blanks can be filled with remaining eight digits in $^8P_2$ ways.
The number of numbers that have $7$ is in thousand place is $3×{^8}P_2=168$
Thousand place cannot be $0,7$ and $3$, it can be filled with remaining $7$ digits in $7$ ways.
In remaining $3$ blanks, $7$ and $3$ can be arranged in $3$ ways.
Fourth blank can be filled in $7$ ways.
The number of numbers that are formed where $7$ and $3$ is not in thousand place is $7×3×7=147$.

Hence total required numbers = $168+147 = 315$