Question

Find the minimum number of students needed to guarantee that 4 of them were born: (a) on the same day of the week;
(b) in the same month

Answer 1

Answer:

hope it helps you mate.

Step-by-step explanation:

Using the pigeonhole principle.

1. There are seven days in a week.
2. If there are 7 students, they could all have been born on different days of the week.

Answer 2

Minimum number of students needed are 22 to guarantee that 4 of them were born on the same day of the week;

minimum number of students needed are 37 to guarantee that 4 of them were born in the same month.

Solution:

4 of them born on the same day of the week

There are 7 days in a week,

Each days can have 3 students before having 4th student born on that day

Hence 7 x 3 = 21 Students

Now 22nd students must be 4th student born on some day

Hence minimum number of students needed are 22 to guarantee that 4 of them were born on the same day of the week.

4 of them  born in same month

There are 12 months in a year

Each month can have 3 students before having 4th student born in that month

Hence 12 x 3 = 36 Students

Now 37th students must be 4th student born on some day

Hence minimum number of students needed are 37 to guarantee that 4 of them were born in the same month.