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Of the members of three athletic teams in a school 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, and 12 play football and cricket. 8 play all the three games. The total number of members in the three athletic teams is
- a)43
- b)76
- c)49
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Of the members of three athletic teams in a school 21 are in the crick...
Let B, H, F denote the set of members who are the basketball team, hockey team and football team, respectively. Then , we are given n (B) = 21, n(H) = 26, n(F) = 29
Thus, these are 43 members in all
Thus, these are 43 members in allMost Upvoted Answer
Of the members of three athletic teams in a school 21 are in the crick...
Let B, H, F denote the set of members who are the basketball team, hockey team and football team, respectively. Then , we are given n (B) = 21, n(H) = 26, n(F) = 29
Thus, these are 43 members in all
Thus, these are 43 members in allFree Test
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Community Answer
Of the members of three athletic teams in a school 21 are in the crick...
Calculation:
To find the total number of members in the three athletic teams, we can use the principle of inclusion-exclusion.
Given data:
- Number of members in the cricket team = 21
- Number of members in the hockey team = 26
- Number of members in the football team = 29
- Number of members playing hockey and cricket = 14
- Number of members playing hockey and football = 15
- Number of members playing football and cricket = 12
- Number of members playing all three games = 8
Using the principle of inclusion-exclusion:
Total members = Members in cricket team + Members in hockey team + Members in football team - (Members playing two games) + (Members playing all three games)
Total members = 21 + 26 + 29 - (14 + 15 + 12) + 8
Total members = 76 - 41 + 8
Total members = 43
Therefore, the total number of members in the three athletic teams is 43, which corresponds to option (a).
To find the total number of members in the three athletic teams, we can use the principle of inclusion-exclusion.
Given data:
- Number of members in the cricket team = 21
- Number of members in the hockey team = 26
- Number of members in the football team = 29
- Number of members playing hockey and cricket = 14
- Number of members playing hockey and football = 15
- Number of members playing football and cricket = 12
- Number of members playing all three games = 8
Using the principle of inclusion-exclusion:
Total members = Members in cricket team + Members in hockey team + Members in football team - (Members playing two games) + (Members playing all three games)
Total members = 21 + 26 + 29 - (14 + 15 + 12) + 8
Total members = 76 - 41 + 8
Total members = 43
Therefore, the total number of members in the three athletic teams is 43, which corresponds to option (a).
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