CAT 2020 Exam Shift 2 Solved Paper

Consider four blanks
_ _ _ _
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 ${}^8{\mathit{P}}_2$ ways. The number of numbers that have 7 is in thousand place is $3{\times }^8{\mathit{P}}_2=168$
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 $7\times 3\times 7=147$. Hence total required numbers $=168+147=315$.