Question

How many numbers superior to 50000 can be formed using the digits 1,2,4,6,8 ?

Answer 1

Conditions

How many numbers superior to 50000 can be formed using the digits 1,2,4,6,8 ?

Solution

If we say about 5-digit number, where all these digits meet only once, there are following numbers exist – all numbers with $1^{\text{st}}$ digit 8 and all numbers with $1^{\text{st}}$ digit 6. Others will be not bigger than 48621 which is less than 50000.

So, let's count how many numbers superior to 50000 exist.

After $1^{\text{st}}$ digit "8" other 4 digits could be chosen in such ways:

$2^{\text{nd}}$ digit – in 4 ways, $3^{\text{rd}}$ – in 3 ways, $4^{\text{th}}$ – in 2 ways, $5^{\text{th}}$ – which is last, 1 way.

That's why the amount of all permutations are:

$$4 - 3 - 2 - 1 = 4! = 24$$

Also, for $1^{\text{st}}$ digit "6" we have 24 permutations too.

Together there are $24 + 24 = 48$ numbers which are superior than 50000.

**Answer: 48**