On the game show Grab That Cash, the contestant is given three envelopes and six bills (three $10 bills, two $20 bills, and one $100 bill). The contestant is told to put the bills in the envelopes in any way they choose (all in one, split evenly, or something else). Then the envelopes are shuffled out of the contestant's sight and brought back out on stage. The contestant chooses an envelope at random and then reaches into it to select a bill at random. How should the contestant place the bills in the envelopes so that the chances are greatest that the contestant will choose the $100 bill?
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.
- On the game show Grab That Cash, the contestant is given three envelopes and six bills (three $10 bills, two $20 bills, and one $100 bill). The contestant is told to put the bills in the envelopes in any way they choose (all in one, split evenly, or something else). Then the envelopes are shuffled out of the contestant's sight and brought back out on stage. The contestant chooses an envelope at random and then reaches into it to select a bill at random. How should the contestant place the bills in the envelopes so that the chances are greatest that the contestant will choose the $100 bill?
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