Pick five pieces of fruit from three bowls with apples, pears and oranges. How many possible combinations are there?
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) Pick five pieces of fruit from three bowls with apples, pears and oranges. How many possible combinations are there?
ii) Determine the probability of winning a third prize in a lottery where you have to select 7 numbers out of 40 distinct numbers. If you pick 4 correct numbers then you win a third prize.
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