Question

The 9 teachers in the Math Department are required to pick a random team out of 30 major league teams to cheer for in the next baseball season. What is the probability that at least two of the teachers have picked the same team?

Answer 1

Given,

Number of teachers = 9

Number of available teachers= 30

Total number of ways = $30\times 30\times30\times.....\times30=30^9$

If all the teachers have picked different number,

then number of ways = $P(30,9)=\dfrac{30!}{21!}$

So,

P( at least two of the teachers have picked the same number ) = 1 - P(each teacher have picked different number) = $1-\dfrac{30!/21!}{30^9}=0.736=\boxed{73.6\%}$