2 a) Six friends together with their respective partners all meet up for a meal. To commemorate the occasion, they arrange for a photograph to be taken of all 12 of them standing in a line. i) How many different arrangements are these if each friend is standing next to his or her partner? ii) How many different arrangements are there if the 6 friends all stand together and the 6 partners all stand together? b) A group of 9 people consists of 2 adults, 3 boys and 4 girls. In how many ways can a team of 4 be chosen if i) both adults are in the team? ii) the girls are either all in the team or all not in the team? iii) at least 2 boys are in the team?
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.
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