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

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 :-)

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

16

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.