Question

The probability that the birthdays of 6 girls will fall on 6 different calender months of a year is

• A. $\frac{1}{{12}^5}$
• B. $\frac{{}^6{C}_6}{{12}^6}$
• C. $\frac{{}^{12}{P}_6}{{12}^6}$
• D. $\frac{1}{{12}^{11}}$

Answer 1

The correct option is C $\frac{{}^{12}{P}_6}{{12}^6}$

Selection of 6 months from the 12 months and then deciding the order of the birthdays of the six girls can be done in ${}^{12}{C}_6\ast 6!$ ways.
The required probability = $\frac{{}^{12}{C}_6\ast 6!}{{12}^6}=\frac{{}^{12}{P}_6}{{12}^6}$