Find the total number of ways of formation of numbers, which are divisible by 3, utilizing 0,1,2,3,4 and 5 without repetition.
Well the question that i was solving asked to find out the number of ways of forming five digit numbers and since I had put a lot of effort in solving it just to find out that i had misread the question, I posted the question here, so as to verify whether my approach is correct or not. Btw I am a noob at combinatorics.
So what I did was as follows:-
1 digit numbers:- 1(i.e. the number 3)
2 digit numbers:-
Lets consider that the number is formed from two digits & and as the number should be a multiple of 3 so,
Now, using multinomial expansion, we get where we have to find the coefficient of
And proceeding forward like this till the six digit numbers. Please do point out any other conditions that i might not have considered here and which would be required in further cases.