Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

The figures 4,5,6,7,8 are written in every possible order. The number of numbers greater than 56000 is?

1) 72

2) 96

3) 90

4) 98

Answer: (3) 90

Solution:

There are in total 5 numbers 4,5,6,7,8.

We need to form numbers greater than 56000

Let us say the number starts with 56_,_,_. Then there are three numbers left that can be arranged in 3! Ways

3! = 6

Similarly, for numbers starting with 57_,_,_ and 58_,_,_.

Hence, 3×6 =18 numbers.

If the number starts with 6, then 6_,_,_,_.

Number of ways 4 digits can be arranged = 4×3×2×1 = 24

In the same way, for 7 and 8, we get 24 for each.

Therefore, total number of numbers greater than 56000 will be

=(24×3)+18

=72+18

=90

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