Number of people who like BOSM = 8800 + (2/5)*3600 = 10240
Number of people who like IOSM = (3/5)*9400 + (2/3)* Number of people who like NOSM -->(1)
Number of people who like NOSM = (3/4)*Number of people who like IOSM -->(2)
Solving (1) and (2), we get, number of people who like IOSM = 11280
Number of people who like NOSM = 8460
Let the number of people who like only one of the three sports competitions be x, those who like exactly two be y and those who like all three be z.
Therefore, x+y+z = 17000 --> (1)
x+2y+3z = 10240+11280+8460 = 29980 --> (2)
Subtracting (1) from (2), we get, y+2z = 12980 -->(3)
Subtracting (3) from (1), we get, x-z = 4020 -->(4)
From (4), minimum value of z possible = 0, in which case x = 4020 and y attains the maximum value = 12980.
Therefore, minimum number of people who like all three sports competitions = 0 and maximum number of people who like exactly two sports competitions = 12980.
From (3), y+2z=12980. Hence, minimum value of y=0 when z=6490. Hence, max and min value of y is 12980 and 0.
