Count the number of possible 8-symbol license plates under the following conditions. State your answers in scientific notation with 4 significant digits. a. For each symbol, use either one of the numerals 0 – 9 or one of the lowercase letters of the alphabet a – z. Symbols may be repeated. ___________ license plates b. For each symbol, use either one of the numerals 0 – 9 or one of the lowercase letters of the alphabet a – z. Symbols may not be repeated. ___________ license plates c. For the first four symbols, use numerals 0 – 9 with repetition and for the last four symbols, use lowercase letters of the alphabet a – z without repetition. ___________ license plates
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.
Count the number of possible 8-symbol license plates under the following conditions.
State your answers in scientific notation with 4 significant digits.
a. For each symbol, use either one of the numerals 0 – 9 or one of the lowercase letters of the alphabet a – z. Symbols may be repeated.
___________ license plates
b. For each symbol, use either one of the numerals 0 – 9 or one of the lowercase letters of the alphabet a – z. Symbols may not be repeated.
___________ license plates
c. For the first four symbols, use numerals 0 – 9 with repetition and for the last four symbols, use lowercase letters of the alphabet a – z without repetition.
___________ license plates
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
