document.write( "Question 1091943: An octapeptide is known to contain four of one amino acid, two of another and two of third. How many different amino acid sequence are possible? \n" ); document.write( "

Algebra.Com's Answer #706463 by greenestamps(13200) $\"\"$ $\"About$

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Sorry to confuse you with (up to now) three different answers to your question....

\n" ); document.write( "You are asking for the number of different arrangements of
\n" ); document.write( " $\"AAAABBCC\"$

\n" ); document.write( "By a well known counting principle, the number of distinct arrangements is
\n" ); document.write( " $\"%288%21%29%2F%28%284%21%29%282%21%29%282%21%29%29+=+420\"$

\n" ); document.write( "If you aren't familiar with that counting principle, here is a quick explanation....

\n" ); document.write( "If all eight items were different, then the number of arrangements would clearly be
\n" ); document.write( " $\"N+=+8%21\"$

\n" ); document.write( "Because 4 items are the same, they can be arranged in 4!=24 different ways that are indistinguishable. So we need to divide the number of distinct arrangements by 4!.
\n" ); document.write( " $\"N+=+%288%21%29%2F%284%21%29\"$

\n" ); document.write( "Because 2 other items are the same, they can be arranged in 2!=2 different ways that are indistinguishable. So we need to further divide the number of distinct arrangements by 2!.
\n" ); document.write( " $\"N+=+%288%21%29%2F%28%284%21%29%282%21%29%29\"$

\n" ); document.write( "Finally, because 2 other items are the same, they can be arranged in 2!=2 different ways that are indistinguishable. So we need to further divide the number of distinct arrangements again by 2!.
\n" ); document.write( " $\"N+=+%288%21%29%2F%28%284%21%29%282%21%29%282%21%29%29\"$

\n" ); document.write( "For another example of the concept, the number of distinct arrangements of the letters MISSISSIPPI (11 letters; 4 the same, 4 others the same, 2 others the same) is
\n" ); document.write( " $\"%2811%21%29%2F%28%284%21%29%284%21%29%282%21%29%29\"$

\n" ); document.write( "Or...

\n" ); document.write( "The number of distinct orders in which you can get 5 heads and 3 tails when you flip a coin 8 times is
\n" ); document.write( " $\"%288%21%29%2F%28%285%21%29%283%21%29%29\"$
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