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
ABC Company considers a new project that has the following cash flow and the required rate of return (WACC) data. What is the project's NPV?Required Rate:10.00%Year0123Ca...
Apr 30 2020In order, list the lenses in the light path between a specimen viewed with the compound light microscope and its image on the retina of the eye.2. What happens to contras...
May 28 2021Imagine that a technological innovation reduces the costs of producing high-quality steel. What happens to the supply curve for steel?2. If the price of cars falls, are c...
Apr 21 2020When 13.66 g of lactic acid, C3H6O3, is mixed with 115 g of stearic acid, the mixture freezes at 62.7 C. The freezing point of pure stearic acid is 69.4 C. What is the fr...
Jun 19 2021On January 1, 2013, Parquet Sales issued 40,000 shares of common stock at a price of $22 per share. The stock has a par value of $1.00 per share. In mid-2014, due to d...
Dec 19 2019Calculate the pOH of a solution that has [H3O] = 3.1 ? 108 MA)pOH = 3.10D)pOH = 3.18B)pOH = 6.49E)pOH = 8.00C)pOH = 7.51102. If the pH of a certain soft drin...
Jan 24 2020Simplify:
Jul 08 2021On June 1, 2015, Irene places in service a new automobile that cost $21,000. The car is used 70% for business and 30% for personal use. (Assume this percentage is maintai...
Mar 22 2020Economies of scale exist when the long run average cost curve is:A) RisingB) FallingC) ConstantD) None of the above
May 12 2021Suppose the threemonth Tbill annualized rate is General Motors Acceptance Corporation GMAC plans to issue commercial paper Their liquidity premium is very low at 0 due t...
Feb 15 2020