Question

The probability that birthday of six different persons will fall in exactly two calendar months is

• A. $\frac{341}{{12}^5}$
• B. ${}^{12}{C}_2\times \frac{2^6-1}{{12}^6}$
• C. ${}^{12}{C}_2\frac{2^6}{{12}^6}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B ${}^{12}{C}_2\times \frac{2^6-1}{{12}^6}$

No. of possible months for a single person = 12
Possible ways for 6 people = ${12}^6$
Birthday falls in two calendar months =
(Choose two months from 12 and then put all the six person into any of the month - the case when all the 6 people get into a single month)
${}^{12}{C}_2.(2^6-1)$
P = $\frac{{}^{12}{C}_2.(2^6-1)}{{12}^6}$