Answer to Question #12447 in Combinatorics | Number Theory for phoebe

Question

in a class of 38 children 19 play tennis, 21play squash and ten students do neither how many children play
a)both sports? b)sqaush? c)tennis?

Answer 1

Let t children play tennіs, s play squash, n do neither and b play both tennis and squash. Then

t + s + n - b = 38 ==> b = t + s + n - 38 = 19 + 21 + 10 - 38 = 50 - 38 = 12.

So, 12 children play both sports, 21 play squash and 19 play tennis.