Question

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DISCRETE STRUCTURES

Note: In each case give justification of solution (i.e. if solution is ()) also write something like: We are choosing subsets of cardinality 2 from a set of cardinality 5)

Answer 1

Solution:-

# number of Students :- 19, 743

Now, The total number of all possible first initial-last initial combinations is 26*26 = 676.

if the total number of students is 677, it simply would mean that at least two person have the same first and last initials.

Therefore, if the number of students is 19,743 , then, # of students having same both initials :- (19743/676)

Which is equal to :- 29.21.

Thus, at least 30 students have same both initials.

b.) Since Leap year comes in every four years, so the average number of days per year:-

(365 + 365 + 365 + 366(Leap year)) / 4 = 365.25 days per year,

Thus, Number of people having the same birthday :- 19743 / 365.25,

Which is approximately equal to :- 54.0533

Therefore, Number of people having the same birthday = 54.

part c.) A described above, If the total number of students is at least 677, it simply would mean that at least two person have the same first and last initials.

also, If the number of students is at least 366, it simply means that at least two studens have birthday, on thae same day.

Therefore, for both to occur, the number of students required is at least, 677*366 = 247,782 Students.

======SOLUTION ENDS==============

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