10 people are in a club. How many ways are there to form a committee consisting of members of the club, such that the committee has at least 2 people in it? How many ways are there to seat the club members in two rows of 5 chairs each, if the club president and vice president don't sit in the same row?
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.
10 people are in a club.
- How many ways are there to form a committee consisting of members of the club, such that the committee has at least 2 people in it?
- How many ways are there to seat the club members in two rows of 5 chairs each, if the club president and vice president don't sit in the same row?
I need the answers of these two questions step by step... Thanks!
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