counting

[lldk]

In using 0,1,2,3,4 and 5 to form a 6-digit number with distinct digits and the first digit cannot be 0, how many cases would result in a number not greater than 324105?

As the question asking, the answer is 2 * 5! + 2 * 4! + 2 * 3! + 2! + 1 = 303. But I can't get the logic of it, can anyone explain it to me?

 

[pka]

In using 0,1,2,3,4 and 5 to form a 6-digit number with distinct digits and the first digit cannot be 0, how many cases would result in a number not greater than 324105? As the question asking, the answer is 2 * 5! + 2 * 4! + 2 * 3! + 2! + 1 = 303. But I can't get the logic of it, can anyone explain it to me?

Take this answer term be term.
\(2\cdot 5!\) counts numbers that begin with a \(1\text{ or }2\)
\(2\cdot 4!\) counts numbers that begin with \(30\text{ or }31\)
\(2\cdot 3!\) counts numbers that begin with what?
continue

 

[lldk]

Take this answer term be term.
\(2\cdot 5!\) counts numbers that begin with a \(1\text{ or }2\)
\(2\cdot 4!\) counts numbers that begin with \(30\text{ or }31\)
\(2\cdot 3!\) counts numbers that begin with what?
continue

begin with 304,314?
then 2! means begin with 3240

 

[pka]

Take this answer term be term.
\(2\cdot 5!\) counts numbers that begin with a \(1\text{ or }2\)

begin with 304,314? then 2! means begin with 3240

@lldk Are you thinking at all?
\(2\cdot 3!\) counts numbers that begin with \(320\text{ or }321\)
\(2!\) counts numbers that begin with \(3240\)
& What?
See HERE

 

[lldk]

@lldk Are you thinking at all?
\(2\cdot 3!\) counts numbers that begin with \(320\text{ or }321\)
\(2!\) counts numbers that begin with \(3240\)
& What?
See HERE

and 1 means begin with 32410[MATH][/MATH]

 

[Steven G]

If the 1st digit is 4 or 5 then the number will certainly be larger than 324105. How many such numbers are there?

If the 1st digit is 0, 1 or 2 then how many numbers will be greater than 324105?

If the 1st digit is 3 then there is more work to be done. Consider the following cases.

The 2nd digit is 0. How many numbers will be greater than 324105?
The 2nd digit is 1. How many numbers will be greater than 324105?
The 2nd digit is 2. How many numbers will be greater than 324105?
The 2nd digit is 4. How many numbers will be greater than 324105?
The 2nd digit is 5. How many numbers will be greater than 324105?