The Gerber County Paintball League has just completed its 10th season. Help the league secretary finalize this year's standings by matching each team to its color, and final ranking. i. The "Night Ninjas" was ranked 1 place ahead of the green team. ii. The group that finished first is either the "Night Ninjas" or the purple team. iii. The "Splat Squad" finished first. iv. The white team was ranked somewhere behind the "Color Blinds". v. The "Color Blinds" finished third. Which is the first, second, third, and fourth in rank? What is the corresponding color of each team?
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.
Problem: The Gerber County Paintball League has just completed its 10th season. Help the league secretary finalize this year's standings by matching each team to its color, and final ranking.
i. The "Night Ninjas" was ranked 1 place ahead of the green team.
ii. The group that finished first is either the "Night Ninjas" or the purple team.
iii. The "Splat Squad" finished first.
iv. The white team was ranked somewhere behind the "Color Blinds".
v. The "Color Blinds" finished third.
Which is the first, second, third, and fourth in rank?
What is the corresponding color of each team?
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