CAT 2020 Question Paper (Slot 2) Question 57

Question 57

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


Correct Answer: 315

Solution

Here there are two cases possible

Case 1: When 7 is at the left extreme

In that case 3 can occupy any of the three remaining places and the remaining two places can be taken by (0,1,2,4,5,6,8,9)

So total ways 3(8)(7)= 168

Case 2: When 7 is not at the extremes

Here there are 3 cases possible. And the remaining two places can be filled in 7(7) ways.(Remember 0 can't come on the extreme left)

Hence in total 3(7)(7)=147 ways

Total ways 168+147=315 ways


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