Algebra II : Permutations
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #11 : Permutations
The soccer team awards gold, silver, and bronze trophies for the top three goal scorers over the season. If the soccer team has 11 players, how many different ways could the gold, silver, and bronze trophies be awarded?
Because the order is important, this is a permutation. There are 11 players to fill 3 spots, so 
Example Question #12 : Permutations
How many possible ways can the letters A and B be assigned to nine people?
Write the formula for permutation.
Evaluate 
Cancel all the common terms in the numerator and denominator.
The answer is:
Example Question #13 : Permutations
Evaluate:
Write the permutation formula.
Substitute the values in the given problem.
Cancel out the terms in the numerator and denominator.
The remaining terms in the numerator are:
The answer:
Example Question #51 : Probability
Evaluate:
Write the permutation formula.
Substitute the values of the variables.
Simplify the factorials.
Cancel the common terms.
The answer is:
Example Question #15 : Permutations
Determine the value of:
Write the permutation formula.
Substitute the values of 
Expand the terms.
Cancel out the terms in the denominator and denominator.
The remaining terms are:
Multiply these numbers.
The answer is:
Example Question #16 : Permutations
Solve the permutation:
Write the formula for permutation.
Substitute the values and expand the factorials.
Reduce the terms.
The answer is:
Example Question #17 : Permutations
Suppose a locksmith designs a three digit lock with numbers ranging only from zero to five. What is the number of permutations possible?
The formula to determine the permutation is:
Notice that for each number, there are 6 different choices since we have numbers ranging from zero to five, not five.
For a three digit lock, 
Substitute the terms into the formula.
The answer is:
Example Question #18 : Permutations
There are 
This is a permutation of 10 objects (runners) taken 3 at a time, with no replacements.
Another way to look at this would be there are 10 runners competing for 1st place, 9 runners competing for 2nd place, and 8 runners competing for 3rd place.
Example Question #61 : Probability
What is the probability of flipping exactly one heads and exactly one tails in two coin tosses?
50%
25%
100%
Cannot be determined
50%
Each of the two coin flips represents one event. The probability of obtaining exactly one heads and exactly one tails can be modeled as follows:
Event 1 * Event 2
The key to understanding this problem is to recognize that either heads followed by tails, or tails followed by heads, would satisfy the specific overall outcome asked for in the problem. Since Event 1 will produce either a heads or a tails, we have a 100% chance of obtaining an outcome from Event 1 that will satisfy one of the two requirements of the specific overall outcome (one heads and one tails). Event 2 will then have a 50% chance of producing an outcome that is the opposite, rather than the same, as the outcome of Event 1. We can therefore calculate the probability of our specific overall outcome as follows:
100% * 50%
1 * 0.5
0.5 = 50%
Therefore, the probability of obtaining one heads and one tails from two coin tosses is 50%.
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