document.write( "Question 1175422: Find the number of ways of arranging all 12 letters of word STRAWBERRIES where
\n" ); document.write( "the first and the last letters are vowels. \n" ); document.write( "
Algebra.Com's Answer #801057 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "The vowels in the word are A, E, E, and I.

\n" ); document.write( "You need to do the calculations as a series of different cases, depending on which vowels are the first and last letters.

\n" ); document.write( "(1) The first and last letters are A and I.

\n" ); document.write( "Those two can be in either of two orders; the remaining 10 letters include 3 R's, 2 S's, and 2 E's. The number of arrangements for this case is

\n" ); document.write( "\"%282%29%2810%21%2F%28%283%21%29%282%21%29%282%21%29%29%29\"

\n" ); document.write( "(2) The first and last letters are A and E.

\n" ); document.write( "Those two can be in either of two orders; the remaining 10 letters include 3 R's and 2 S's. The number of arrangements for this case is

\n" ); document.write( "\"%282%29%2810%21%2F%28%283%21%29%282%21%29%29%29\"

\n" ); document.write( "(3) The first and last letters are I and E.

\n" ); document.write( "This case will have the same number of arrangements as case (2).

\n" ); document.write( "(4) The first and last letters are E and E.

\n" ); document.write( "There is only one way to arrange those; the remaining 10 letters include 3 R's and 2 S's. The number of arrangements for this case is

\n" ); document.write( "\"10%21%2F%28%283%21%29%282%21%29%29\"

\n" ); document.write( "Add the numbers of arrangements for the four cases to get the final answer.

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