![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
Since you say \"combinations\", order does not matter.\r\n" );
document.write( "\r\n" );
document.write( "However I still can't tell which of two possibilities you want.\r\n" );
document.write( "The correct solution is either choice (a) or choice (d).\r\n" );
document.write( "\r\n" );
document.write( "If you mean selecting 4 DIFFERENT letters, there\r\n" );
document.write( "are only 8 different letters in COMBINATION, which\r\n" );
document.write( "are {A,B,C,I,M,N,O,T}, and that is\r\n" );
document.write( "\r\n" );
document.write( "8C4 = 70 choice (a)\r\n" );
document.write( "\r\n" );
document.write( "Here they all are, 7 rows of 10 each in alphabetical\r\n" );
document.write( "order: \r\n" );
document.write( "\r\n" );
document.write( "ABCI ABCM ABCN ABCO ABCT ABIM ABIN ABIO ABIT ABMN\r\n" );
document.write( "ABMO ABMT ABNO ABNT ABOT ACIM ACIN ACIO ACIT ACMN\r\n" );
document.write( "ACMO ACMT ACNO ACNT ACOT AIMN AIMO AIMT AINO AINT\r\n" );
document.write( "AIOT AMNO AMNT AMOT ANOT BCIM BCIN BCIO BCIT BCMN\r\n" );
document.write( "BCMO BCMT BCNO BCNT BCOT BIMN BIMO BIMT BINO BINT\r\n" );
document.write( "BIOT BMNO BMNT BMOT BNOT CIMN CIMO CIMT CINO CINT\r\n" );
document.write( "CIOT CMNO CMNT CMOT CNOT IMNO IMNT IMOT INOT MNOT\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "However if you allow such as AIIN or NNOO, where\r\n" );
document.write( "we can choose two Is, two Ns, or two O's, then the\r\n" );
document.write( "answer is 136, choice (d).\r\n" );
document.write( "\r\n" );
document.write( "Here's how to work that:\r\n" );
document.write( "\r\n" );
document.write( "Case 1: All four are different letters:\r\n" );
document.write( "\r\n" );
document.write( "8C4 = 70 (Same as the problem as interpreted above)\r\n" );
document.write( "\r\n" );
document.write( "Case 2: There is exactly one pair of like letters.\r\n" );
document.write( "\r\n" );
document.write( "Choose the letter of which there will be two of from {I,N,O}\r\n" );
document.write( "That's 3C1 = 3 ways. \r\n" );
document.write( "That leaves 7 letters to choose for the remaining two letters:\r\n" );
document.write( "That's 7C2 = 21\r\n" );
document.write( "So there are 3*21 = 63 \r\n" );
document.write( "\r\n" );
document.write( "Case 3: There are two pairs of like letters.\r\n" );
document.write( "Choose 2 from {I,N,O}\r\n" );
document.write( "\r\n" );
document.write( "That's 3C2 = 3 ways\r\n" );
document.write( "\r\n" );
document.write( "Total from the 3 cases: 70+63+3 = 136, choice (d)\r\n" );
document.write( "\r\n" );
document.write( "Here they all are. 13 rows of 10 each and the bottom\r\n" );
document.write( "row has only 6, in alphabetical order:\r\n" );
document.write( "\r\n" );
document.write( "ABCI ABCM ABCN ABCO ABCT ABII ABIM ABIN ABIO ABIT\r\n" );
document.write( "ABMN ABMO ABMT ABNN ABNO ABNT ABOO ABOT ACII ACIM\r\n" );
document.write( "ACIN ACIO ACIT ACMN ACMO ACMT ACNN ACNO ACNT ACOO\r\n" );
document.write( "ACOT AIIM AIIN AIIO AIIT AIMN AIMO AIMT AINN AINO\r\n" );
document.write( "AINT AIOO AIOT AMNN AMNO AMNT AMOO AMOT ANNO ANNT\r\n" );
document.write( "ANOO ANOT AOOT BCII BCIM BCIN BCIO BCIT BCMN BCMO\r\n" );
document.write( "BCMT BCNN BCNO BCNT BCOO BCOT BIIM BIIN BIIO BIIT\r\n" );
document.write( "BIMN BIMO BIMT BINN BINO BINT BIOO BIOT BMNN BMNO\r\n" );
document.write( "BMNT BMOO BMOT BNNO BNNT BNOO BNOT BOOT CIIM CIIN\r\n" );
document.write( "CIIO CIIT CIMN CIMO CIMT CINN CINO CINT CIOO CIOT\r\n" );
document.write( "CMNN CMNO CMNT CMOO CMOT CNNO CNNT CNOO CNOT COOT\r\n" );
document.write( "IIMN IIMO IIMT IINN IINO IINT IIOO IIOT IMNN IMNO\r\n" );
document.write( "IMNT IMOO IMOT INNO INNT INOO INOT IOOT MNNO MNNT\r\n" );
document.write( "MNOO MNOT MOOT NNOO NNOT NOOT\r\n" );
document.write( "\r\n" );
document.write( "You'll have to ask your teacher which answer \r\n" );
document.write( "he/she wants.\r\n" );
document.write( "\r\n" );
document.write( "Edwin \n" );
document.write( "