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 hockeyand 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 isa)43b)76c)49d)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

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

Answer

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).

Similar Mathematics Doubts

Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is

Out of 16 players of cricket team, 4 are bowlers and 2 are wicket keepers. A team of 11 players is to be chosen so as to contain at least 3 bowlers and atleast one wicket keeper. The number of ways in which the team be selected is

In a football championship, 153 matches were played. Every team played one match with each other. The number of teams participating in the championship is

Two towns A and B are 60 km apart. A school is to be built, to serve 150 students from town A and 50 students from town B. If the total distance travelled by all 200 students is to be as small as possible, then the school should be built at

Top Courses for Mathematics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams