Question

If numbers are formed using digits 2, 3, 4, 5,
6 without repetition, how many of them will
exceed 400?​

Answer 1

There are 276 numbers greater than 400 .

Explanation:

The given digits = 2, 3, 4, 5,  6

Total digits = 5

To make three-digits numbers greater than 400 , we need to fix first place for 4 , 5 , 6 and the rest of 2 places can be filled in 4! choices.

So , Number of three-digits numbers greater than 400= 3 x 4 x 3

= 36

Using permutations,

Number of four-digits numbers ( all greater than 400) = $^5P_4=\dfrac{5!}{(5-4)!}=120$

Number of five-digits numbers ( all greater than 400) = 5!=120

Total numbers greater than 400= 36+120+120 =276

Therefore , there are 276 numbers greater than 400 .

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