First, let's solve the subtraction (in parentheses):
Now, let's solve the multiplication. Remember: in multiplication, two negative numbers will give a positive number:
Finally, let's solve the division:
Part A
Since order matters, we use the nPr permutation formula
We use n = 12 and r = 8
There are a little under 20 million different permutations.
<h3>Answer: 19,958,400</h3>Side note: your teacher may not want you to type in the commas
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Part B
In this case, order doesn't matter. We could use the nCr combination formula like so.
We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.
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Another way we can compute the answer is to use the result from part A.
Recall that:
nCr = (nPr)/(r!)
If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320
So,
Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.
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<h3>Answer: 495</h3>