document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=491882>Question 491882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that (m+n)Ck = mCk * nC0 + mC(k-1) * nC1 + mC(k-2) * nC2 + ... + mC0 * nCk<BR>\n" );
document.write( "For k <= (m+n) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334815 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=334815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose Committee A has m people and Committee B has n people, and we want to choose a total of k people out of the total m+n. We can choose all k people from Committee A and none from Committee B, for mCk*nC0 ways. Or we can choose k-1 people from A and 1 person from B, and so on, hence the given statement is true.\r<BR>\n" );
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document.write( "However, this only works for k <= m and k <= n, unless we define xCy = 0, if x < y. </SPAN>\n" );
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