CAT 2020 Quant Question [Slot 2] with Solution 15

Question

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

Option: 315
Solution:

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 \(^8{P_2}\) ways. The number of numbers that have 7 is in thousand place is \(3{ \times ^8}{P_2} = 168\)

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 \(7 \times 3 \times 7 = 147\). Hence total required numbers \( = 168 + 147 = 315\).

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CAT 2020 Quant questions with Solutions