My Math Forum multinomial combination question

 January 24th, 2010, 05:20 PM #1 Member   Joined: Jan 2010 Posts: 43 Thanks: 0 multinomial combination question The question verbatim is: 8 new teachers are to be divided among 4 schools, how many divisions are possible? The answer is 65536 but I can't seem to arrive at this many divisions. Any help or incite would be great!
January 24th, 2010, 07:49 PM   #2
Math Team

Joined: Dec 2006
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Re: multinomial combination question

Hello, meph1st0pheles!

Quote:
 8 new teachers are to be divided among 4 schools. How many divisions are possible? (The answer is 65536.)

$\text{For each of the 8 teachers, there are 4 choices of schools.}$

$\text{Hence, the number of possible assignments is: }\:4^8 \:=\:65,536$

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