I have done an exercise but I am not sure for the result. Could you help me with it if it right or wrong? The exercise:
I have a university and I have students ages $18$ to $25$. At least how many people should be in a trip to ensure there will be at least $10$ persons with the same age and the same sex (men and women).
What I did was $\frac x{20} =10$ so $x=10 \cdot 20 = 200$. $x$ is the whole persons and I divide by $20$ because $10$ women and $10$ men. Am I right? Wrong? What?
Thanks.
There are 8 age groups and two sexes.
There can be at most 9 in each group without reaching the desired position.
Therefore you must have $8\times2\times9+1=145$ people.