Answer: 96 played one sport only.
Explanation:
To find out how many played one sport only, we can use the principle of inclusion-exclusion.
Let S be the total number of sports men surveyed. Then, we have:
S = number who played soccer + number who played volleyball + number who played basketball - number who played soccer and volleyball - number who played soccer and basketball - number who played volleyball and basketball + number who played all three sports
Substituting the given values, we get:
S = 64 + 94 + 58 - 28 - 26 - 22 + 14
S = 154
Therefore, there were 154 sports men surveyed in total.
Now, let x be the number of sports men who played one sport only. Then, we have:
x = number who played soccer only + number who played volleyball only + number who played basketball only
Substituting the given values and using the principle of inclusion-exclusion, we get:
x = (64 - 28 - 26 + 14) + (94 - 28 - 22 + 14) + (58 - 26 - 22 + 14)
x = 22 + 58 + 24
x = 104
Therefore, there were 104 sports men who played one sport only.
Note that this includes those who did not play any of the three sports. To find out how many played at least one sport, we can subtract the number who did not play any sport from the total number surveyed:
number who played at least one sport = total number surveyed - number who did not play any sport
number who played at least one sport = 154 - (S - x)
number who played at least one sport = 154 - (154 - 14)
number who played at least one sport = 14
Therefore, there were 14 sports men who did not play any of the three sports.
Finally, to find out how many played one sport only, excluding those who did not play any sport, we can subtract 14 from 104:
number who played one sport only, excluding those who did not play any sport = 104 - 14
number who played one sport only, excluding those who did not play any sport = 90
Therefore, there were 90 sports men who played one sport only, excluding those who did not play any sport.