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How many words can be formed from the word SAMARINDA, if
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document.write( "The letters in alphabetical order are AAADIMNRS\r\n" );
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document.write( "Case 1: All 4 letters come from {D,I,M,N,R,S}\r\n" );
document.write( "6P4=360 ways.\r\n" );
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document.write( "Case 2: Exactly 1 A and 3 letters from {D,I,M,N,R,S}\r\n" );
document.write( "An example would be SAND.\r\n" );
document.write( "Choose the 3 non-A letters from {D,I,M,N,R,S} in 6C3=20 ways.\r\n" );
document.write( "Arrange the 4 letters in 4P4=4!=24 ways.\r\n" );
document.write( "That's 20∙24=480 ways for case 2.\r\n" );
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document.write( "Case 3: Exactly 2 A's and 2 letters from {D,I,M,N,R,S}.\r\n" );
document.write( "An example would be ADAM\r\n" );
document.write( "Choose the 2 non-A letters from {D,I,M,N,R,S} in 6C2=15 ways\r\n" );
document.write( "Arrange the 4 letters in 4!/2!=24/2=12 ways\r\n" );
document.write( "That's 15∙12=180 ways for case 3. \r\n" );
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document.write( "Case 4: Exactly 3 A's and 1 letter from {D,I,M,N,R,S}.\r\n" );
document.write( "An example would be ABAA\r\n" );
document.write( "Choose the 1 non-A letters from {D,I,M,N,R,S} in 6C1=6 ways\r\n" );
document.write( "Put it in any of 4 positions.\r\n" );
document.write( "That's 6∙4=24 ways for case 4.\r\n" );
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document.write( "Total for the three cases: 360+480+12+24=1044\r\n" );
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document.write( "ii) only 3 letters can be used.\r\n" );
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document.write( "Case 1: Exactly 0 A's and all 3 letters from {D,I,M,N,R,S}\r\n" );
document.write( "An example would be RIM.\r\n" );
document.write( "Choose and position the 3 non-A letters from {D,I,M,N,R,S} in 6P3=6∙5∙4=120\r\n" );
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document.write( "That's 120 ways for case 1.\r\n" );
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document.write( "Case 2: Exactly 1 A and 2 letters from {D,I,M,N,R,S}.\r\n" );
document.write( "An example would be AIR\r\n" );
document.write( "Choose the 2 non-A letters from {D,I,M,N,R,S} in 6C2=15 ways\r\n" );
document.write( "Arrange the 3 letters in 3!=6 ways\r\n" );
document.write( "That's 15∙6=90 ways for case 1. \r\n" );
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document.write( "Case 3: Exactly 2 A's and 1 letter from {D,I,M,N,R,S}.\r\n" );
document.write( "An example would be ADA\r\n" );
document.write( "Choose the 1 non-A letter from {D,I,M,N,R,S} in 6C1=6 ways\r\n" );
document.write( "Put it in any of 3 positions.\r\n" );
document.write( "That's 6∙3=18 ways for case 1.\r\n" );
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document.write( "Case 4: Exactly 3 A's\r\n" );
document.write( "The only one is AAA.\r\n" );
document.write( "That's 1 way for case 4\r\n" );
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document.write( "Total for the four cases: 120+90+18+1=229\r\n" );
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document.write( "Edwin \n" );
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