Answer:
[tex]\dfrac{4}{33}[/tex].
Step-by-step explanation:
Given information:
Total number of students = 11
Number of boys = 6
Number of girls = 5
It is given that they have no matched birthdays.
We select 3 eldest students. So, the total number of ways are
[tex]^{11}C_3=\dfrac{11!}{(11-3)!3!}=165[/tex]
Possible ways of selecting 3 eldest students are all boys.
[tex]^{6}C_3=\dfrac{6!}{(6-3)!3!}=20[/tex]
So, the probability that 3 eldest students are all boys is
[tex]P=\dfrac{20}{165}=\dfrac{4}{33}[/tex]
Therefore, the required probability is [tex]\dfrac{4}{33}[/tex].
