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The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students?
  • a)
    23
  • b)
    91
  • c)
    60
  • d)
    49
  • e)
    None of the above.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The rules for the University of Bombay five-a-side cricket competition...
There are 12 months and we have to get 5 people having birthdays in the same month in order to form a team . we can apply the pigeon hole principal :
[N/12] = 5
On solving we get N=49 .
Hence answer is D.
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Most Upvoted Answer
The rules for the University of Bombay five-a-side cricket competition...

Minimum number of mathematics students needed:

To guarantee that a team of students with birthdays in the same month can be formed, we need to consider the worst-case scenario where each group of students has birthdays in different months. We can use the Pigeonhole Principle to determine the minimum number of mathematics students needed.

Explanation:

- Since there are 12 months in a year, we need at least 12 students to ensure that there is at least one student in each month.
- However, for a five-a-side cricket team, we need 5 students in the same month to form a team.
- Therefore, we need to find the smallest multiple of 5 that is greater than 12, which is 15.
- This means that we need a minimum of 15 mathematics students enrolled in the department to guarantee that they can raise a team of students with birthdays in the same month.

Minimum number of mathematics students needed = 15

Therefore, option 'D) 49' is the correct answer as it provides more than enough students to form multiple teams with birthdays in the same month.
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The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students?a)23b)91c)60d)49e)None of the above.Correct answer is option 'D'. Can you explain this answer?
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