Question

In a group of \[8\] students. What is the probability of each one of them having birthdays on the different day of the week?

Answer 1

Hint:Here we count the number of students and number of days in a week and then using the concept of probability we try to find the probability.

Complete step-by-step answer:
Since we know the number of students are \[8\].
Number of days in a week is \[7\]
To find the probability of each student having birthday on different days of the week we mean finding the probability of \[8\] students having their birthday on \[7\] different days.
Since, number of students is greater than number of days in a week
i.e. \[8 > 7\]
Using the formula for probability
Probability \[ = \] number of favorable outcomes/ total number of outcomes
Probability will be \[ = \dfrac{7}{8}\] which is greater than one
Since, we know probability is always greater than zero and less than or equal to one, therefore, in this situation probability is zero.

Note:Students are likely to make mistake of doing this question using combination method where they might attempt to form combinations for one student's birthday on how many days is possible which is wrong.
* Always keep in mind Probability is less than or equal to one
Alternate Method:
Number of students is \[8\] and the number of days in a week is \[7\].
The number of students is greater than the number of days in a week.
Therefore, it is impossible for \[8\] students to have their birthdays on \[7\] different days of a week because one student's birthday will always be with someone else on the same day.