A student visits a sports club everyday from monday to friday after scholl hours and plays one of the three games:Cricket,Tennis,Football.In how many ways can he play each of tje 3 games atleast once during a week?

Answer 1

Consider counting from 00000 to 22222 in base 3. There are 3^5 = 243 different values.
We can consider just 81 of these, since however we treat the 0's can also be done for the 1's and 2's.

Of the 81 numbers that have 0's, there is just 1 that is all 0's.

That leaves 80, some of which have no 1's or no 2's.

There are 15 with no 1's, and 15 with no 2's. So, that means there are 50 that have 0,1,2.

Replace 0 with 1 or with 2 and reason the same, so there are 150 different ways to play at least one of the sports during the 5-day week.

I'm sure some combinatorics expert out there that has a better formula.