Question

A mint prepares metallic calenders specifying months, dates, days in the form of monthly sheets ( one plate for each month). How many types of calenders should it prepare to serve for all the possibilities in the future years

Answer 1

In the future years, a month can have 28, 29, 30 or 31 days.
So types of months = 4
A month can start from any day of the week.
So any month can have 7 types of starting.

So total types of calender = 7×4 = 28

Answer 2

See

There are two types of year

A leap year and a non-leap year

In a leap year february has 29 days

Where in a non-leap year it has 28 days

So they are counted as '2' possibilities either 28 or 29

Then every year starting day and ending day can not be the same

So the starting or ending day can be any day of the weak ie any of the 7 days and accordingly the calendar will also change so here we have '7' possibilities

Now apply multiplication principle of p and c

We get

7× 2 = 14 different types for the future years.

Thank you :-)

And the answer is 14 only

The above ans need a correction

Every year the months have fixed days except february so :)