Berechne
4!2!\frac{4!}{2!}2!4!
4!2!=4⋅3⋅2⋅12⋅1= 4⋅3 =12\frac{4!}{2!}=\frac{4\cdot3\cdot2\cdot1}{2\cdot1}=\;4\cdot3\;=122!4!=2⋅14⋅3⋅2⋅1=4⋅3=12
4!2!=4⋅42⋅2=164=4\frac{4!}{2!}=\frac{4\cdot4}{2\cdot2}=\frac{16}4=42!4!=2⋅24⋅4=416=4
4!2!=4⋅32⋅1 = 122=6\frac{4!}{2!}=\frac{4\cdot3}{2\cdot1}\;=\;\frac{12}2=62!4!=2⋅14⋅3=212=6
4!2!=4⋅12⋅1 = 2\frac{4!}{2!}=\frac{4\cdot1}{2\cdot1}\;=\:22!4!=2⋅14⋅1=2
9!5!\frac{9!}{5!}5!9!
9!5!=9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅15⋅4⋅3⋅2⋅1=9⋅8⋅7⋅61=3024\frac{9!}{5!}=\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5\cdot4\cdot3\cdot2\cdot1}=\frac{9\cdot8\cdot7\cdot6}1=30245!9!=5⋅4⋅3⋅2⋅19⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1=19⋅8⋅7⋅6=3024
9!5!=9⋅55⋅4=94\frac{9!}{5!}=\frac{9\cdot5}{5\cdot4}=\frac945!9!=5⋅49⋅5=49
9!5!=9⋅85⋅4=9⋅25⋅1=185\frac{9!}{5!}=\frac{9\cdot8}{5\cdot4}=\frac{9\cdot2}{5\cdot1}=\frac{18}55!9!=5⋅49⋅8=5⋅19⋅2=518
9!5!=9⋅95⋅5=8125\frac{9!}{5!}=\frac{9\cdot9}{5\cdot5}=\frac{81}{25}5!9!=5⋅59⋅9=2581
5!⋅7!8!\frac{5! \cdot 7!}{8!}8!5!⋅7!
5!⋅7!8!=(5⋅4⋅3⋅2⋅1)⋅(7⋅6⋅5⋅4⋅3⋅2⋅1)8⋅7⋅6⋅5⋅4⋅3⋅2⋅1=5⋅4⋅3⋅2⋅18=5⋅3⋅11=15\frac{5!\cdot7!}{8!}=\frac{(5\cdot4\cdot3\cdot2\cdot1)\cdot(7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}=\frac{5\cdot4\cdot3\cdot2\cdot1}8=\frac{5\cdot3\cdot1}1=158!5!⋅7!=8⋅7⋅6⋅5⋅4⋅3⋅2⋅1(5⋅4⋅3⋅2⋅1)⋅(7⋅6⋅5⋅4⋅3⋅2⋅1)=85⋅4⋅3⋅2⋅1=15⋅3⋅1=15
5!⋅7!8!=5⋅5⋅7⋅78⋅8=122564\frac{5!\cdot7!}{8!}=\frac{5\cdot5\cdot7\cdot7}{8\cdot8}=\frac{1225}{64}8!5!⋅7!=8⋅85⋅5⋅7⋅7=641225
5!⋅7!8!=5⋅4⋅7⋅68=5⋅4⋅7⋅68=5⋅1⋅7⋅62=105\frac{5!\cdot7!}{8!}=\frac{5\cdot4\cdot7\cdot6}8=\frac{5\cdot4\cdot7\cdot6}8=\frac{5\cdot1\cdot7\cdot6}2=1058!5!⋅7!=85⋅4⋅7⋅6=85⋅4⋅7⋅6=25⋅1⋅7⋅6=105
5!⋅7!8!=5⋅8⋅7⋅88⋅8=5⋅71=35\frac{5!\cdot7!}{8!}=\frac{5\cdot8\cdot7\cdot8}{8\cdot8}=\frac{5\cdot7}1=358!5!⋅7!=8⋅85⋅8⋅7⋅8=15⋅7=35
2!⋅3!9!\frac{2!\cdot3!}{9!}9!2!⋅3!
2!⋅3!9!=2⋅1⋅3⋅2⋅19⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1=2⋅19⋅8⋅7⋅6⋅5⋅4=19⋅8⋅7⋅6⋅5⋅2=130240\frac{2!\cdot3!}{9!}=\frac{2\cdot1\cdot3\cdot2\cdot1}{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}=\frac{2\cdot1}{9\cdot8\cdot7\cdot6\cdot5\cdot4}=\frac1{9\cdot8\cdot7\cdot6\cdot5\cdot2}=\frac1{30240}9!2!⋅3!=9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅12⋅1⋅3⋅2⋅1=9⋅8⋅7⋅6⋅5⋅42⋅1=9⋅8⋅7⋅6⋅5⋅21=302401
2!⋅3!9!=2⋅39⋅1=69=23\frac{2!\cdot3!}{9!}=\frac{2\cdot3}{9\cdot1}=\frac69=\frac239!2!⋅3!=9⋅12⋅3=96=32
2!⋅3!9!=2⋅2⋅3⋅3⋅39⋅9⋅9⋅9⋅9=2⋅2⋅19⋅9⋅9⋅3=42187\frac{2!\cdot3!}{9!}=\frac{2\cdot2\cdot3\cdot3\cdot3}{9\cdot9\cdot9\cdot9\cdot9}=\frac{2\cdot2\cdot1}{9\cdot9\cdot9\cdot3}=\frac4{2187}9!2!⋅3!=9⋅9⋅9⋅9⋅92⋅2⋅3⋅3⋅3=9⋅9⋅9⋅32⋅2⋅1=21874
2!⋅3!9!=2⋅39⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1=19⋅8⋅7⋅6⋅5⋅4=160480\frac{2!\cdot3!}{9!}=\frac{2\cdot3}{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}=\frac1{9\cdot8\cdot7\cdot6\cdot5\cdot4}=\frac1{60480}9!2!⋅3!=9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅12⋅3=9⋅8⋅7⋅6⋅5⋅41=604801
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