There are 15 students at a party. Five of them are boys and ten are girls in how many ways can they be arranged in a row if i)there are no restrictions, ii)the five boys have to stay next to each other iii)no pair of boys is adjacent iv)between two particular girls, Alice(A) and Bernadette(B), there are no girls and exactly three boys?
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.
There are 15 students at a party. Five of them are boys and ten are girls in how many ways can they be arranged in a row if
i)there are no restrictions,
ii)the five boys have to stay next to each other
iii)no pair of boys is adjacent
iv)between two particular girls, Alice(A) and Bernadette(B), there are no girls and exactly three boys?
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