Question

The probability that out of $5$ persons, all having birthday in March, at least two have the same birthday

• A. $\frac{{}^{31}{\text{C}}_5}{{\left(31\right)}^5}$
• B. $\frac{{\left(31\right)}^5{-}^{31}{\text{C}}_5}{{\left(31\right)}^5}$
• C. $\frac{{\left(31\right)}^3{-}^{31}{\text{C}}_5}{{\left(31\right)}^5}$
• D. None of these

Answer 1

The correct option is B $\frac{{\left(31\right)}^5{-}^{31}{\text{C}}_5}{{\left(31\right)}^5}$

Number of days in month of March=31
n(S) = ${31}^5$
n(A)= at least two have the same birthday
=n(S) Number of ways in which all candidates have the different birthday
=${31}^5$ - ${}^{31}{C}_5$
P ={ ${31}^5$ - ${}^{31}{C}_5$ }/ ${31}^5$