A certain game consists of two steps. First, a standard die is rolled, and thenumber showing is recorded. If the number is even, then a coin is tossed,and its result is recorded. Otherwise, a card is drawn from a standarddeck, and the suit is recorded.(a) How many different outcomes are there for this game?(b) Is the number of outcomes involving a coin the same as the numberinvolving a card? Explain.
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.
A certain game consists of two steps. First, a standard die is rolled, and the
number showing is recorded. If the number is even, then a coin is tossed,
and its result is recorded. Otherwise, a card is drawn from a standard
deck, and the suit is recorded.
(a) How many different outcomes are there for this game?
(b) Is the number of outcomes involving a coin the same as the number
involving a card? Explain.
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