Question

Find the no. ways in which an even number less than 3,000,000 can be formed using digits 1,2,2,3,5,5,6

Answer 1

can digits be repeated?

Answer 2

Yes

Answer 3

Are the additional 2s and 5s typos, then? Because it seems redundant to include them otherwise.

Answer 4

well this comes under permutations with repetitions

Answer 5

permutations with identical elements

Answer 6

Hmm, well then I suppose this is how I would structure the problem, but forgive me because I don't remember the precise equations.
Figure out the number of permutations using any 6,5,4,3,2, and 1 digit(s). There are no limits on this, because the largest of them will still be less than 3,000,000. Now you can still make a few 7-digit numbers less than 3,000,000. Namely, any 7-digit numbers starting with 1 or 2. That gives you 3 options for your first digit, and then 6 for the rest.

Answer 7

Sorry I couldn't give any more precise help :/

Answer 8

I know that the first digit has to be either 1 or 2, the next 5 digits can be anything, and the last digit has to be 2 or 6

Answer 9

but the two 2's is what is giving some trouble for the 1st and the last digit

Answer 10

why does the last digit ever have to be a 2 or a 6?

Answer 11

because we want an even number

Answer 12

Oh man, my bad. I didn't even see that part of the question!
Do you have to use all of the digits?

Answer 13

yes

Answer 14

Ok, one more question for you, are the '2's unique? For example, is 122 different than 122 if I use the twos in a different order?

Answer 15

I think they should still be the same

Answer 16

Ok, then you have (2) options, 1 and 2, for the first digit (2) options, 2 and 6, for the last digit and 5 options for everything inbetween.

Answer 17

i think in between we have more than just 5 options