document.write( "Question 847245: How many distinct permutations can be made out of the word \"CONCOCTION\" that begins and ends with letter \"C\"? \n" ); document.write( "

Algebra.Com's Answer #510305 by swincher4391(1107) $\"\"$ $\"About$

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Fix the first and last letters to be C.\r
\n" ); document.write( "\n" ); document.write( "How many different letters can the 2nd spot be? 8\r
\n" ); document.write( "\n" ); document.write( "3rd? 7\r
\n" ); document.write( "\n" ); document.write( "4th? 6\r
\n" ); document.write( "\n" ); document.write( "5th? 5\r
\n" ); document.write( "\n" ); document.write( "etc.\r
\n" ); document.write( "\n" ); document.write( "9th? 1\r
\n" ); document.write( "\n" ); document.write( "We have 8! ways to arrange, but we need to factor out the order to get distinctness.\r
\n" ); document.write( "\n" ); document.write( "There are 3 Os, 2 Ns, 1 C, 1 T and 1 I. We really only need to concern ourselves with these multiple letters (O and N)\r
\n" ); document.write( "\n" ); document.write( "There is 3! ways to order the Os.\r
\n" ); document.write( "\n" ); document.write( "There is 2! ways to order the Ns.\r
\n" ); document.write( "\n" ); document.write( "So our total distinct permutations is 8! / (3! * 2!) [which is a variation of our multinomial formula]. This gives us 3360.\r
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