Question

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3.
[This Question was asked as TITA]

• A. 462
• B. 513
• C. 315
• D. 295

Answer 1

Answer: (C)

315

Answer 2

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 $3×^8P_2=168$
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 = $168+147 = 315$

So, the correct option is (C): $315$