Your club would like to form a committee that has 2 sophomores, 3 juniors, and 4 seniors. If there are 7 sophomores, 8 juniors, and 6 seniors in the club, how many different ways can the committee be formed? Assume that the order that you are picked in does not matter.
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.
In this question out of 7 sophomores we have to choose 2, Out of 8 juniors, we have to choose 3 and out of 6 seniors, we have to choose 4. Since the order does not matter we can use combinations to find the answer.
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