# What is the number of numbers that can be made from the numbers two and three such that the number contains 4 digits?

Feb 22, 2016

${2}^{4} = 16$
There are $2$ possibilities for the first digit (either two or three).
For each of those $2$ possibilities there are $2$ possibilities for the second digit for a combination of $2 \times 2 = 4$ possibilities for the first two digits.
For each of those $4$ possibilities there are $2$ possibilities for the third digit, for a combination of $4 \times 2 = 8$ possibilities for the first three digits.
For each of those $8$ possibilities there are $2$ possibilities for the four digit, for a combination of $8 \times 2 = 16$ possibilities for the four digits.