Question

The probability that the birthdays of 12 girls will fall on 12 different calender months of a year is

• A. $\frac{1}{{12}^{11}}$
• B. $\frac{{}^{12}{C}_{12}}{{12}^{12}}$
• C. $\frac{{}^{12}{P}_{12}}{{12}^{12}}$
• D. $\frac{1}{{12}^5}$

Answer 1

The correct option is C $\frac{{}^{12}{P}_{12}}{{12}^{12}}$

Lets say we are assigning a birth-month to those 12 girls.
Given no restriction, we can do that in ${12}^{12}$ ways.
If we want each one to have a birthday in a different month, then it is as if we are permuting $12$ months among $12$ girls.
We can do this in ${}^{12}{P}_{12}$ ways.
Hence, the answer.