How many four-digit numbers can be formed from the digits 1 and 2 if repetitions are allowed?

And what is the best way of working it out, other than just listing all the possibilities?

Thanks!

Dragon.Jade2012-03-28T09:01:48Z

Favorite Answer

Hello,

First digit is either 1 or 2, hence you have two possibilities...
Second digit is either 1 or 2, hence you have again two possibilities...
Third digit is either 1 or 2, hence you have yet again two possibilities...
Last digit is either 1 or 2, hence you have guess what? Two possibilities...

So the total number of all possibilities is:
2 × 2 × 2 × 2 = 16 possibilities.

No need to list them all.

Logically,
Dragon.Jade :-)

Muammar2012-03-28T09:01:28Z

in the required four digit number,
the ones place may be a 1 or a 2
----- possibilites = 2
the tens place may be a 1 or a 2
-----possibilities = 2 * 2
the hundreaths place may be a 1 or a 2
----- possibilities = 2 * 2 * 2
the thousandths place may be a 1 or a 2
-----possibilities = 2 * 2 * 2 * 2
= 16

Thus, there are 16 possibilities

Amber2012-03-28T09:57:08Z

16

Crazins2012-03-28T09:02:31Z

n is number of objects so n=2 and r is the number of choices so r=4 so n^r so 2^4=16. 16 possibilities.