analise combinatoria.pdf - Prof Marcelo Renato
analise combinatoria.pdf - Prof Marcelo Renato
analise combinatoria.pdf - Prof Marcelo Renato
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n<br />
+<br />
r − 1<br />
<br />
n<br />
r<br />
=<br />
= n![r!(n − r)!] + n![(r − 1)!(n − r + 1)!]<br />
= n!r!(n − r)! + n!(r − 1)!(n − r + 1)!<br />
= n!r(r − 1)!(n − r)! + n!(r − 1)!(n − r + 1)(n − r)!<br />
= n!r + n!(n − r + 1)<br />
= n!(r + n − r + 1)<br />
=<br />
=<br />
=<br />
Fórmula de Pascal<br />
n!<br />
(r − 1)!(n − r + 1)! +<br />
n!<br />
r!(n − r)!<br />
r!(n − r + 1)!(r − 1)!(n − r)!<br />
r!(n − r + 1)!(r − 1)!(n − r)!<br />
r!(n − r + 1)!<br />
r!(n − r + 1)!<br />
n!(n + 1)<br />
r!(n − r + 1)!<br />
(n + 1)!<br />
r!(n − r + 1)!<br />
<br />
n + 1<br />
r<br />
r!(n − r + 1)!(r − 1)!(n − r)!<br />
UFMG/ICEx/DCC Matemática Discreta 90
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