Question

The number of possible outcomes in a throw of $n$ ordinary dice in which at least one of the dice shows an odd number is

• A. $6^{n-1}$
• B. $3^n-1$
• C. $6^n-3^n$
• D. none of these

Answer 1

The correct option is C $6^n-3^n$

Total number of possible outcomes in a throw of $n$ ordinary dies $=6\times 6\times 6\times 6\times .................n-times=6^n$
The even numbers in the throw of an ordinary dice are $2,4,6$
The total number of possible outcomes when no dice show odd number $=3\times 3\times 3\times 3\times .............n-times=3^n$
Hence the number of possible outcomes in which at least one dice shows an odd number$=${Total possible outcomes-possible outcomes when no dice shows an odd number}
$=6^n-3^n$
Hence, option 'C' is correct.