Home / Questions / In how many ways can 4 people be seated in a row of 12 chairs I broke the question down i...
In how many ways can 4 people be seated in a row of 12 chairs?
I broke the question down into 2 parts, then solved them and multiplied the answer to get 11,880 ways.
We can solve this by breaking down the question into 2 smaller questions. The first question is "how many ways can we choose 4 chairs out of 12 to have someone sit in" and the second question is "how many ways can 4 people sit in 4 chairs". Our final answer will be the product of the 2 smaller questions.
The first smaller question - "how many ways can we choose 4 chairs out of 12 to have someone sit in" - is a combinations question (how many ways can we pick 4 chairs from a group of 12) - that is written in a few different notations - I'll write it out as Combination 12 choose 4 and in notation ##C_(12,4)##
For each combination of 4 chairs selected out of the 12, there are different ways the people can sit in them - we can have persons A B C D, or A B D C, etc. There are, in fact ##4!## ways each selection of chairs can be sat in.
Our final answer, therefore is
##(4!)(C_(12,4))##
Let's solve
##(4!)=4*3*2*1=24##
##(C_(12,4))=(12!)/((4!)(8!))=(12*11*10*9*8!)/((24)(8!))=(12*11*10*9)/24##
Now let's combine the 2:
##(24)((12*11*10*9)/24)=(12*11*10*9)=11,880##
Apr 03 2020 View more View Less
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