Question

The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is 15 K then K is equal to ................

Answer 1

There are in total $6$ numbers, $4,5,6,7,8$.
Now consider the number
$56000$
Consider the numbers of the form
$56---$.
Considering no repetitions we get
$3\times 2\times 1$
$=6$ numbers.
Similarly for $57---$ and $58---$.
Hence
$3\times 6$
$=18$ numbers.
Now consider the numbers starting with 6.
$6----$
We get $4\times 3\times 2\times 1$
$=24$.
Similarly for the numbers starting with 7 and 8 we get in total 24 numbers each.
Hence total number of numbers greater than 56000 will be
$=(24\times 3)+18$
$=72+18$
$=90$

$15K=90\Rightarrow K=6$