Counting Principle

[Pingu]

The question is: How many even two-digit whole numberscan be made using the digits 1,2,3,4,5,6,7, and 8. Repetitions are not allowed.

 

[Unco]

G'day, Pingu.

An even number must end with an even digit. Try writing down all the possibilities for a number ending with 2 from the given digits. Can you see a pattern emerging?

 

[soroban]

Hello, Pingu!

How many even two-digit whole numbers can be made using the digits 1,2,3,4,5,6,7, and 8.
Repetitions are not allowed.

The units-digit must be even; there are four choices: {2,4,6,8}.

The tens-digit can be any of the other seven digits.

Answer: \(\displaystyle \,4\,\times\,7\:=\:28\) possible even two-digit numbers.

 

[mathfun]

the unit digits can be even or odd.
for odd, there are 4 choices. [1,3,5,7]
therefore, odd would have 4 choices as well and it has to be even [2,4,6,8]

for unit digits to be even, there are 4 choices. [2,4,6,8]
however, since repetitions are not allowed, tens digits only have 3 choices.

therefore...
4x4 + 4x3 = 16 + 12 = 28

 

[Pingu]

Thanks, I was able to do the question.