Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words.How many ways can the letters of GIWLEG be arranged? What is the probability of coming up with the correct unscrambling through random letter selection? (Type an integer or simplified fraction.)
Question
Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words.How many ways can the letters of GIWLEG be arranged? What is the probability of coming up with the correct unscrambling through random letter selection? (Type an integer or simplified fraction.)
Solution
The number of ways the letters of GIWLEG can be arranged is calculated by finding the factorial of the number of letters. Since there are 6 letters in GIWLEG, the total number of arrangements is 6! (6 factorial), which is 65432*1 = 720.
However, since the letter G and the letter W each appear twice, we have to divide the total by 2! for each of these repetitions to avoid counting duplicate arrangements. So the final number of unique arrangements is 720 / (2!*2!) = 180.
The probability of coming up with the correct unscrambling (i.e., the word GIWLEG) through random letter selection is 1 out of the total number of possible arrangements. So the probability is 1/180.
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