Word Scramble
Type fast!
Find all the anagrams as you can, but you gotta be quick to get the maximum score!
Think fast!
Then answer the counting/probability question to proceed.
Find all the anagrams as you can, but you gotta be quick to get the maximum score!
Then answer the counting/probability question to proceed.
Suppose n is a positive integer. When we say n "factorial", we mean to multiply it by every positive integer below it. We represent this function with an exclamation mark !
For instance, 5! = 5 × 4 × 3 × 2 × 1 = 120
("5 factorial" equals 120)
Rearranging all the letters in a word is a type of "permutation" function (choosing items in a specific order).
If the word has n distinct letters, there are n! ways to rearrange the letters (though not all of these will be real words).
For instance, "AMONG" has 5! = 120 permutations of all 5 letters, even though many of these, like GNMAO are "non-words".
The basic formula to determine a probability is:
| # of results in consideration |
| total # of possible results |
Example: "If the letters of GAMES are randomly scrambled, what is the probability that the result will be MAGES or GASME."
There are 2 results in consideration (MAGES or GASME), and 5! total possible results of scrambling this 5 letter word, so the answer is 2/5!
Note: this answer could also be written as:
How many different ways can we order all the letters shown in TESLA? (It doesn't matter if the result is a real word.)
If a computer randomly rearranges all the letters shown in TESLA, what is the probability that they will end up in the same order as the starting order, TESLA?
If a computer randomly rearranges all the letters shown in TESLA, what is the probability that the result will be one of your (accepted) answers for this problem?
The correct answer is: 1/1! = 0.00
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