Question

The probability that the birth days 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. $\frac{{}^{12}{P}_{12}}{{12}^6}$

Answer 1

Answer: (C)

$\frac{{}^{12}{P}_{12}}{{12}^{12}}$

there are $12$ months available for each girl to be born
Hence total possible cases = ${12}^{12}$
If all the $12$ girls have to be born in different months, then we have to distribute $12$ months in $12$ girls where each will get one. No. of ways of doing this = $12!$