Question

# of red sides showing #0f sticks tossed 0 1 2 3 4 5 6 7 Tablh /. Each cell of the table contains the number of ways of tossing a certain number of sticks and getting a certain number of red sides. 1.2 Binomial coefficients. The boardgames Senet (Egypt) and The Royal Game of Ur (Mesopotamia) predate Zeno and Archimedes by well over a thousand years. In some versions of these games, the players tossed sticks rather than dice; each stick was two-sided, like a small popsicle stick, one side painted red, the other painted white. The number of red sides showing indicated the number of pieces the player could move. For example, say that a player tosses three sticks. With the sticks labeled A, B and C for convenience, we observe that there are three ways that the sticks will 12 The Anoients allow a player to move two pieces: the red sides can show on sticks AB, sticks AC, or sticks BC. Following this reasoning, we can fill in the first row of Table 1 (a) Fill in the rest of the table (b) As you do so, look for any patterns you see, and express your observation in words. (c) Argue on behalf of your observation in 1.2(b). One way to do this is to consider the fate of one of the sticks: is it white, or is it red? This breaks your counting problem into two cases

Need help answering part A-C of this Calc question.

Answer 1

Fact: Out of n distinguishable objects, the number of ways to choose k many objects is given by the Binomial Co-efficient

$\binom{n}{k}$