Question

How many 6 digit numbers (in base 10) have all their digits in the set {8,9}?

Please show work that leads to the answer.

Answer 1

first digit have 2 chances namely 8 or 9,

second digit have 2 chances namely 8 or 9,

third digit have 2 chances namely 8 or 9,

fourth digit have 2 chances namely 8 or 9,

fifth digit have 2 chances namely 8 or 9 and

sixth digit have 2 chances namely 8 or 9,

Hence number of  6 digit numbers (in base 10) have all their digits in the set {8,9} are $2\times 2\times 2\times 2\times 2\times 2=2^{6}=64$