Use the following information to answer the next three questions. A bag contains five different balls colored Red, White, Blue, Yellow, and Green. You cannot see into the bag and you cannot tell the balls apart by feel. 1. If two balls are selected at random without replacement, how many different permutations are possible? 2. If two balls are selected at random without replacement, how many combinations are possible? 3. If two balls are selected at random with replacement, what is the probability (to nearest 0.0001) of NOT getting Yellow on any of the picks?
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.
Use the following information to answer the next three questions. A bag contains five different balls colored Red, White, Blue, Yellow, and Green. You cannot see into the bag and you cannot tell the balls apart by feel.
1. If two balls are selected at random without replacement, how many different permutations are possible?
2. If two balls are selected at random without replacement, how many combinations are possible?
3. If two balls are selected at random with replacement, what is the probability (to nearest 0.0001) of NOT getting Yellow on any of the picks?
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