How many even numbers can be formed from these 3 digits?

probability combinatorics statistics combinations

2,281

Solution 1

For a number to be even it must end in a even digit $2$ or $4$ so $2$ choices. The second digit can be any of the $4$ digits which wasn't used as the last digit, and the first digit can be any except those $2$ which were used as the second and third digit hence $3$ choices, all in all we get $2\cdot 4\cdot 3=24$.

Solution 2

kingW3 answer is absolutely correct. I'm not debating on his answer, just answering in the way the question has been asked.

Selecting either 2 or 4 from the Set for the unit place as the no. should be even: 2C1
Selecting the digit from the left over digits for the tens place: 4C1
Selecting the digit from the left over digits for the hundreds place: 3C1

Therefore we get, 3C1 x 4C1 x 2C1 = 24

The thing you have done 5C1 x 4C1 x 3C1 would have been correct if you were asked to make any 3 digits no from the given set without repeating.

I apologize if the repeating of an answer is not allowed.

2,281

Admin

Updated on August 01, 2022

Comments

Admin over 1 year

Digits: 1, 2, 3, 4, 5

Q: how many even 3 digit numbers can be made without repeating them?

In total, I worked out that there's 60 three digit numbers that can be made without repeating (5C1 x 4C1 x 3C1) = 60.

But, I have no idea about the even bit. Could somebody talk me through it so I can understand?

Thanks!
- Admin about 6 years
  
  the title of the question is malformed just a hint.
Admin about 6 years

Thanks! Could you clarify something? For digit one, I pick one of the even numbers (e.g. 2). For digit 2, I can pick any digit that I didn't just use? So, 1, 3, 4 or 5? (e.g. 5). And for the third digit, I use any that I haven't used previously? I.e. 1, 3, 4? Because in this situation, 2 x 5 x 4 = 40, which is different to 24.
kingW3 about 6 years

@MathsHelp That's right, though keep in mind that digit one is the last digit (or the first one from right). How do you get 2 x 5 x 4? You have $2$ choices for the first(last) digit and then 4 digits for the second and 3 for the last.
Admin about 6 years

Oh, sorry, I think I misinterpreted your words. I thought you meant from my set of numbers that I could literally pick any. I get it now, thanks! If I were to change the question slightly and I had 1, 2, 3, 4, 5 and 6, would it be 3 x 5 x 4 instead of 2 x 4 x 3?
kingW3 about 6 years

@MathsHelp Exactly it would be $3\times 5\times 4$.
Admin about 6 years

just to be sure, 24 is the final answer isn't it? You don't deduct this from 60 to get 36 as the final answer?