Yes.
You can carry red pen in 4 ways and blue pen in 2³ = 8 ways
Delete cases don't carry at all. There are ways to carry (4×8)-1 = 31 ways.
Yes.
You can carry red pen in 4 ways and blue pen in 2³ = 8 ways
Delete cases don't carry at all. There are ways to carry (4×8)-1 = 31 ways.
How to organise a tournament between 3 participants such that it doesn't give any one undue advantage, and doesn't rely on tie breaker.
One idea that immediately pops up is to match them against on another and who wins most wins the tourney. To illustrate let the participants be called A, B, and C. So A plays B, then A plays C, then B plays C. In this there is no dismay, that the tournament can theoretically go for eternity, say A plays B, A wins. A plays C, C wins. B plays C, B wins. Now what? Each team has won one match and are equal? Who is your winner? This obviously doesn't work
Problem 17:
There are 4 different blue pens and 3 identical red pens. Find the number of ways to carry at least one pen.
All red pen are the same, so the red pen can be carried in only 4 ways (0,1,2 or 3).