1. how many three-letter code symbols can be formed using a set of 5 different letters in repetion is not allowed?
2. Mark can remember only the first 5 digits of his friends phone number. He also knows that the number has 7 digits and that the last digit is not 0. If mark were to dial all of possible numbers and if takes him 20 seconds to try each one, how long would it take to try every possbility?
Please I need help with this two questions I'm reviewing for my test for next week. Thanks
1. The first space of the code can be filled in 5 ways
the second place in 4 ways, and the third place in 3 ways.
So the number of codes = 5x4x3 = 60
2. So we only have to worry about the last two numbers,
the second last can be filled in 10 ways, (10 numerals), but the last one in only 9 ways, (no zero)
so there are 90 differrent permutations he has to try
and if it takes 20 seconds per try .....
then what do I divide 90 by 20? But then I will come up with 4.5 and that is not one of my mult. choice answers.
1. To find the number of three-letter code symbols that can be formed using a set of 5 different letters with no repetition allowed, we can use the concept of permutations.
In this case, we need to select and arrange 3 letters from a set of 5. The number of ways to do this is given by the formula for permutations, which is:
P(n, r) = n! / (n - r)!
Where n is the total number of elements to choose from, and r is the number of elements to select. In our case, n = 5 and r = 3.
P(5, 3) = 5! / (5 - 3)!
= 5! / 2!
= 5 * 4 * 3
= 60
Therefore, there are 60 different three-letter code symbols that can be formed using a set of 5 different letters without repetition.
2. To calculate the time it would take for Mark to try every possible number, we need to determine the total number of possible numbers and multiply it by the time it takes to dial each one.
Given that Mark can remember the first 5 digits and the last digit is not 0, we have 10 choices (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for the first 5 digits, and 9 choices (1, 2, 3, 4, 5, 6, 7, 8, 9) for the last digit.
The total number of possible numbers is given by multiplying the number of choices for each digit:
Total number of possible numbers = 10 * 10 * 10 * 10 * 10 * 10 * 9 = 900,000
Since it takes Mark 20 seconds to try each number, we can determine the total time it would take by multiplying the total number of possible numbers by 20:
Total time = 900,000 * 20 = 18,000,000 seconds
Therefore, it would take Mark 18,000,000 seconds to try every possible number.