A soap company will give away a million dollars to everyone who guesses the order into which they have arranged the letters of the word SUPERCLEANER. Each entry must be in a separate envelope. How much would it cost you in postage to submit all possible entries?
SUPERCLEANER
12 letters including 3E's and 2R's
Number of ways to arrange them = 12!/(2!3!) = 39916800
Multiply that by the postage per letter in your country, which I don't know.
Yes I did 39916800X0.57 which is our postage per letter
In a particular business, everyone has a three-letter designation after their name in which the letters are not repeated. What is the smallest number of people employed by the business if there must be at least two people with the same three-letter designation?
To determine the cost of postage for submitting all possible entries, we need to calculate the number of arrangements of the letters in the word "SUPERCLEANER."
The word "SUPERCLEANER" consists of 12 letters, with some repeated letters. To find the number of arrangements, we can use the concept of permutations with repetition.
First, let's determine the total number of arrangements if all the letters were distinct. Since there are 12 letters, the number of arrangements would be 12! (12 factorial), which equals 479,001,600.
However, we need to account for the repeated letters in "SUPERCLEANER."
The letter "E" appears twice, "R" appears twice, and "A" appears twice. To correct the overcounting caused by the repeated letters, we divide the total number of arrangements by the factorial of the number of repetitions for each letter.
The letter "E" appears twice, so we divide by 2!
The letter "R" appears twice, so we divide by 2!
The letter "A" appears twice, so we divide by 2!
The corrected number of arrangements is:
12! / (2! * 2! * 2!) = 76,824,960
So there are 76,824,960 possible arrangements of the letters in "SUPERCLEANER."
Now, let's calculate the cost of postage.
Assuming each entry must be in a separate envelope, we need to determine the cost of postage for one entry and then multiply it by the number of possible entries.
The cost of postage for one entry depends on the postal rates in your region. Let's say it costs $0.50 to mail one envelope.
To calculate the total cost, we multiply the cost of mailing one entry by the number of possible entries:
Total cost = Cost of one entry * Number of possible entries
Total cost = $0.50 * 76,824,960
Therefore, it would cost $38,412,480 in postage to submit all possible entries.