Question

Find the total natural numbers that can be formed by using the digits 0, 1, 2, 3, 4, and 5 , repetition of the digits is not allowed.

Answer 1

102345
123450
234501
345012
451023
501234
134502
345210
453210
543210
Such more numbers can be formed

Answer 2

Note :
1. Zero can't be in first place. that is if a two digit no. begin with 0 it's a one digit no.
2. Everything is just based on assumption and imagination.

First let us assume the case of 1 digit no. = 5

Now, forming two digit no.
In tenth place we can have 5 ( 1,2,3,4,5) numbers and in one's place assuming one no. is at tenth place ( let say 4) we have balance 5 no. left (0,1,2,3,5).
So, we have 5× 5 = 25

Now, forming three digit no.
In hundredths place we have 5 (1,2,3,4,5) no.
and in tenth place assuming one no. is at hundredths place we have (let say 3) we have balance 5 no. (0,1,2,4,5). And in ones place we have 4no. (0,1,4,5) left after 1 no. gone in tenths place ( let say 2)
So we have 5×5×4 = 100

Now, forming four digit no.
In thousands place 5 no. (1,2,3,4,5) (and assume 1 is in thousands place)
in hundredths place 5 no.( 0,2,3,4,5) ( and assume 2 is in hundredths place)
in tenths place 4 no. (0,3,4,5) ( and assume 3 is in tenths place)
in one's place 3 no. (0,4,5)
So, 5×5×4×3 = 300

Now, forming 5 digit no.
in ten thousands place we have 5 no.
in thousands place we have 5 no.
in hundredths place we have 4no.
in tenth place we have 3 no.
in one's place we have 2 no.
So, 5×5×4×3×2 = 600

Now, forming 6 digit no.
In lakhs place we have 5 no.
in ten thousands place we have 5 no.
in thousands place we have 4 no.
in hundredths place we have 3 no.
in tenth place we have 2 no.
in one's place we have 1 no.
So, 5×5×4×3×2×1 = 600

Final answer = adding all digits answer
= 5+25+100+300+600+600
= 1630 no. can be formed