The coach of a basketball tema wants a plan B just in case all of her starters foul out in a game. The starting team consists of A, B, C, D, and E, and the substitute squad consists F, G, H, I, J, and K. F can substitute for either A or B, G can substitute for either B or C, H can substitute for either A, C, or D, I can substitute for either C or D, J can substitute for wither D or E, and K can substitute for E. A. Model the possible substitutions on the team using a bipartite graph. B. Find a matching for the first team, if all of them foul out in a game.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
The coach of a basketball tema wants a plan B just in case all of her starters foul out in a game. The starting team consists of A, B, C, D, and E, and the substitute squad consists F, G, H, I, J, and K. F can substitute for either A or B, G can substitute for either B or C, H can substitute for either A, C, or D, I can substitute for either C or D, J can substitute for wither D or E, and K can substitute for E.
A. Model the possible substitutions on the team using a bipartite graph.
B. Find a matching for the first team, if all of them foul out in a game.
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