A school dance committee is made up of 2 freshman, 5 sophomores, 2 juniors, and 5 seniors. How many ways are there to sit the committee in a row at a meeting if the students must sit together by grade? How many ways are there to sit the committee in a row at a meeting if the freshman,sophomores, and juniors must sit by grade, but the seniors can sit wherever they want?
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.
A school dance committee is made up of 2 freshman, 5 sophomores, 2 juniors, and 5 seniors.
How many ways are there to sit the committee in a row at a meeting if the students must sit together by grade?
How many ways are there to sit the committee in a row at a meeting if the freshman,sophomores, and juniors must sit by grade, but the seniors can sit wherever they want?
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