Question

A professor tells three jokes in his ethics course each year. How large a set of jokes does the professor need in order never to repeat the exact same triple of jokes over a period of 12 years?

Answer 1

1st year we need 3 jokes

2nd year 1 more

And this 1 can combine in 3 ways

So 3rd 4th year we not need any new joke

Now 5th year add 1 more

Now it can combine in 4 ways so

6th 7th 8th year we not need new jokes

Nom 9th year add 1 more

Now it can combine in 5 ways so

10th 11th 12th year we not need any new jokes.

Hence we need total 6 jokes (3for 1st yr,1 in 2nd,1 in 5th and 1 1 in 9th year)

By using combination

nC3 is equal to 12

Now by using combination formula n>6 hence at least 6 jokes are reqired