Question

Show that in any group of 30 people, we can always find 5 people who were born on the same day of the week.

Answer 1

Answer:Nice 1

Step-by-step explanation:

Answer 2

There will be 5 people who were born on the same day of the week.

GIVEN

Total number of people = 30

TO FIND

To show that there are always 5 people who were born on the same day of the week.

SOLUTION

We can simply solve the above problem as follows;

Number of People in a group = 30.

According to the Generalised Pigeonhole Theorem.

If 'n' items are required to be put in 'm' containers, where n > m, then atleast 1 container has more than one one container.

Now,

Number of people(n) = 30

Number of days in a week(m) = 7

Number of people born on same day of the week = (30/7) + 1

= 4.28 + 1

= 5.2 ≈ 5

Hence, There will be 5 people who were born on the same day of the week.

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