How to do 206th question?

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3 Answers
Mar 28, 2018

Answer: (22) 10!10!

Explanation:

1010 men and 1010 women to form 1010 male-female couples.

Let the 1010 men be fixed and the females be deciding how the couples will be matched.

The 1^(st)1st woman will be able to choose between 1010 man.

The 2^(nd)2nd woman will be able to choose between 99 man.

The 3^(rd)3rd woman will be able to choose between 88 man.

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.
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The 10^(th)10th woman will be able to choose between 11 man.

Hence, the number of possible outcomes will be,

10xx9xx8xx7xx6xx5xx4xx3xx2xx1=10!10×9×8×7×6×5×4×3×2×1=10!

Therefore, there is 10!10! number of ways to divide 1010 man and 1010 woman into 1010 male-female couples.

Mar 30, 2018

See the response from my associate:

Explanation:

The question is slightly ambiguous in that it does not tell us whether the division into couples is ordered or not. In practice, the only option that works is 2) 10! with the understanding that the order of the couples does not matter. Given that, each man in turn could choose 1 woman in turn, so 10 choices for the first man 9
for the second, etc, giving 10! possible divisions into 10
couples.

Mar 30, 2018

Solution Part 2 of 2
Investigating value.

Logically you would expect a whole number solution and the only one giving that is option 2

Explanation:

color(blue)("Which option do we select ?")Which option do we select ?

color(green)("Option 1") color(red)(larr" Not a whole number !")Option 1 Not a whole number !

color(white)()^20 C_10->(n!)/((n-r)!r!) ->(20!)/((20-10)!10!)=(20!)/((10!)^2)20C10n!(nr)!r!20!(2010)!10!=20!(10!)2

(cancel(20)^2xx19xxcancel(18)^2xx17xxcancel(16)^2xxcancel(15)^3xxcancel(14)^2xx13xxcancel(12)^2xx11xxcancel(10!))/((cancel(10)^1xxcancel(9)^1xxcancel(8)^1xxcancel(7)^1xxcancel(6)^1xxcancel(5)^1xx4xx3xx2)cancel(10!))

color(white)("ddddddddddd")(19xx13xx11)/(24) = 113.208

color(white)()

color(green)("Option 2")color(blue)(larr" A whole number !")

10! =10xx9xx8xx7xx6xx5xx4xx3xx2=3628800

color(white)()

color(green)("Option 3")color(red)(larr" Not a whole number !")

(10!)/2^10

(cancel(10)^5xx9xxcancel(8)^4xx7xxcancel(6)^3xx5xxcancel(4)^2xx3xxcancel(2))/ (cancel(2)xxcancel(2)xxcancel(2)xxcancel(2)xxcancel(2)xx2xx2xx2xx2xx2)

(5xx9xxcancel(2)^1xx7xx3xx5xx3)/(cancel(2)xx2xx2xx2xx2)=885.9375

color(white)()

color(green)("Option 4")color(red)(larr" Not a whole number !")
color(white)()

(9!)/2^10

(9xxcancel(8)xx7xxcancel(6)^3xx5xxcancel(4)xx3xxcancel(2))/(2xx2xx2xxcancel(2)xxcancel(2)xxcancel(2)xxcancel(2)xxcancel(2)xxcancel(2)xxcancel(2) )

(9xx7xx3xx5xx3)/(2^3) = 354.375

color(white)()

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Let's have a look at the other answer provided by

Numeros fous color(red)(larr" Not a whole number !")

(10(10+1)[2(10+1)])/6 = 10/3xx11^2 = 403 1/3