Question

There are 2000 students in a school and they all play atleast 2 of the 5 sports - Cricket, Badminton, Hockey, Table Tennis (TT) and Football. It is also known that no. of students playing in every combination of exactly two sports is 4 times the no. of students playing in every combination of exactly 3 sports. Also, no. of students playing all the 5 sports is 1/4" of those playing exactly 4 sports. The number of students playing in every combination of exactly 4 sports is the s
ame.If the number of people playing all the 5 spo is 160, then what is the no. o students playing only cricket & football? (1) 72 (3) 480 (2) 116 (4) 96​

Answer 1

Answer:

480 is the right answer I think

Answer 2

Answer:

96

Explanation:

students Playing 5 sports = y and combination of it is 5c5 so 1 way = 5y

students Playing 4 sports = 4y and combination of it is 5c4 so 5 ways = 20y

students Playing 3 sports = x and combination of it is 5c3 so 10 ways = 10x

students Playing 2 sports = 4x and combination of it is 5c2 so 10 ways = 40x

adding all

5x+20y+10x+40x= 2000

y+2y= 80

given in question 5y= 160

y= 32

y+2x=80

32 + 2x= 80

x= 24

only cricket and football= (24×40)/10 = 96