In an​ orchestra, 22 people can play stringed​ instruments, 17 can play​ brass,15 and can play percussion.​ Further, 8 of the performers can play both strings and​ brass, whereas 7 can play both strings and percussion. If no one can play all three types of​ instruments, what are the maximum and minimum numbers of people in the​ orchestra? ​(Hint​: Consider expressing the numbers in some of the regions of your diagram in terms of a single​ unknown, say​ x.)