A company issues a questionnaire whereby each employee must rank the 5 items with which he or she is most satisfied. The items are wages, work environment, vacation time, job security, supervisors, health insurance, break time, and retirement plan.
The ranking is to be indicated by the numbers 1, 2, 3, 4 and 5, where
1 indicates the item involving the greatest satisfaction and 5 the least.
In how many ways can an employee answer this questionnaire?
First we need to find n and r :
If you said n is 8 you are correct!!!
There are 8 items listed.
r is the number of items we are ranking at a time. What do you think r is?
If you said r is 5, pat yourself on the back!! We are ranking the top 5.
Putting this into the permutation formula we get:
*Expand 8! until it gets to 3! ( which is the ! in den)
*Cancel out 3!'s
If you don't have a factorial key, you can simplify it as shown above and then enter it in. It is probably best to simplify it first, because in some cases the numbers can get rather large, and it would be cumbersome to multiply all those numbers one by one.
Wow, this means there are 6720 different ways to rank these items.
A key pad lock has 10 different digits, and a sequence of 5 different
digits must be selected for the lock to open. How many key pad combinations
are possible?
First we need to find n and r :
If you said n is 10 you are correct!!!
There are 10 digits.
r is the number of digits being used at a time. What do you think r is?
If you said r is 5, pat yourself on the back!! There are 5 digits in the sequence.
Putting this into the permutation formula we get:
*Expand 10! until it gets to 5! ( which is the ! in den)
*Cancel out 5!'s
If you don't have a factorial key, you can simplify it as shown above and then enter it in. It is probably best to simplify it first, because in some cases the numbers can get rather large, and it would be cumbersome to multiply all those numbers one by one.
Wow, this means there are 30240 different combinations.
In how many ways can 7 books be arranged on a shelf?
First we need to find n and r :
If you said n is 7 you are correct!!!
There are 7 books in this problem.
r is the number of books we are using at a time. What do you think r is?
If you said r is 7, pat yourself on the back!! We are arranging all 7 books on the shelf.
Putting this into the permutation formula we get:
*0! = 1
*Expand out 7!
If you don't have a factorial key, you can simplify it as shown above and then enter it in. It is probably best to simplify it first, because in some cases the numbers can get rather large, and it would be cumbersome to multiply all those numbers one by one.
Wow, this means there are 5040 different ways to arrange these books.
Last revised on May 16, 2011 by Kim Seward.
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