Considering that a choir group is made up of ten boys and fifteen girls.How many ways are there to select a committee with 6 members if it must have 1.At least 1 girl and at least 1 boy? 2.At most 3 girls ii)How many serial numbers on a phone battery can be made utilizing either 2 or 3 letters followed by either2 or 3 numbers and contain no letter or number twice?
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.
i)Considering that a choir group is made up of ten boys and fifteen girls.How many ways are there to select a committee with 6 members if it must have
1.At least 1 girl and at least 1 boy?
2.At most 3 girls
ii)How many serial numbers on a phone battery can be made utilizing either 2 or 3 letters followed by either2 or 3 numbers and contain no letter or number twice?
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