Diketahui n+1​P3​=14×n​C2​. Tentukan: a.   nilai n;  b.   hasil n+1​Cn−2​.

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Diketahui . Tentukan:

a.   nilai 

b.   hasil 

  1. .... 

  2. .... 

F. Ayudhita

Master Teacher

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Pembahasan

Ingat:

1. begin mathsize 14px style P presubscript n subscript r equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction end style

2. begin mathsize 14px style C presubscript n subscript r equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial times r factorial end fraction end style

 

a.   nilai begin mathsize 14px style n end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P presubscript n plus 1 end presubscript subscript 3 end cell equals cell 14 cross times C presubscript n subscript 2 end cell row cell fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator left parenthesis open parentheses n plus 1 close parentheses minus 3 right parenthesis factorial end fraction end cell equals cell 14 cross times fraction numerator n factorial over denominator left parenthesis n minus 2 right parenthesis factorial times 2 factorial end fraction end cell row cell fraction numerator left parenthesis n plus 1 right parenthesis times n factorial over denominator left parenthesis n minus 2 right parenthesis factorial end fraction end cell equals cell 14 cross times fraction numerator n factorial over denominator left parenthesis n minus 2 right parenthesis factorial times 2 times 1 end fraction end cell row cell n plus 1 end cell equals 7 row n equals 6 end table end style

 

b.   hasil begin mathsize 14px style C presubscript n plus 1 end presubscript subscript n minus 2 end subscript end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C presubscript n plus 1 end presubscript subscript n minus 2 end subscript end cell equals cell C presubscript left parenthesis 6 plus 1 right parenthesis end presubscript subscript left parenthesis 6 minus 2 right parenthesis end subscript end cell row blank equals cell C presubscript 7 subscript 4 end cell row blank equals cell fraction numerator 7 factorial over denominator left parenthesis 7 minus 4 right parenthesis factorial times 4 factorial end fraction end cell row blank equals cell fraction numerator 7 times 6 times 5 times 4 factorial over denominator 3 times 2 times 1 times 4 factorial end fraction end cell row blank equals cell 7 times 5 end cell row blank equals 35 end table end style

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Diketahui pernyataan-pernyataan berikut. (i)    n​Pr​=n​Pn−r​  (ii)   n​Cr​=n​Cn−r​  (iii)  n​Pr​=r×n​Cr​ Pernyataan yang benar adalah ....

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