How do you simplify $_{10} P_{8}$ $""_10P_8$ ?

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Answer 1 · 2017-05-06T10:56:26

$(10!)/(2!)=(10xx9xx8xx7xx6xx5xx4xx3xxcancel2)/cancel2=1,814,400$

The permutation general formula is:

$P_(n,k)=(n!)/((n-k)!); n="population", k="picks"$

and so the question is how to calculate:

$P_(10,8)=(10!)/((10-8)!)=(10!)/(2!)$

There are two ways to do it:

We can look up the values on a chart (I use the one at https://www.mathsisfun.com/numbers/factorial.html), and so $10! = 3,628,800 and 2! = 2$ , giving us:

$(3,628,800)/2=1,814,400$

$(10xx9xx8xx7xx6xx5xx4xx3xxcancel2)/cancel2=1,814,400$

How do you simplify ""_10P_810P8""_10P_8?