Haven't done a problem like this in a while but from what I remember:

Find how many play 1 sport first

Basketball

Start with 17-8(baseball and basketball)-5(basketball and football)=4 students play just basketball

Baseball

Start with 21-8(both bballs) -6(football and baseball)=7 play just baseball

Football

Start with 24-6-5=13 play just Football

So far we have 13+7+4=24 students

Add that to the double sport players

24+8+5+6=43 students play sports

Another way is to take 21+17+24=6s and subtract the doubles

62-8-5-6=43