Question

Suppose a subset of eight different days of the year is selected at random. What is the probability that each day is from a different month

Answer 1

P = 0.05

Explanation:

12 months * 30 days each = 360 days

From 306 days, we have to select 8 days = 360C8 ways(Total ways)

We want each days from different month. First, we have to select 8 month from 12 month = 12C8 ways

---By selecting 8 month, we will select a days from each month. That can be done in = 30C1 * 30C1 * .................30C1 (8 ways) [From a month with 30 days, we can select a day in 30C1 ways = 30 ways]

Therefore P = Number of ways of selecting each days from different month / Total number of ways

P = 12C8 * 30^8 / 360C8

P = 495 * 656100000000 / 6469697679132645

P = 0.0501985588982791

P = 0.05

Hence the probability that each day is from a different month is 0.05