4 mothers with four children walk in for a interview. Find the no of ways
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document.write( "to schedule this interview such that no child is interviewed before
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document.write( "her mother.
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document.write( "Suppose that:\r\n" );
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document.write( "mother A1 has daughter A2, and\r\n" );
document.write( "mother B1 has daughter B2, and\r\n" );
document.write( "mother C1 has daughter C2, and\r\n" );
document.write( "mother D1 has daughter D2.\r\n" );
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document.write( "Then I claim the answer is the same as the number of\r\n" );
document.write( "distinguishable permutations of AABBCCDD, which is\r\n" );
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document.write( "Why?\r\n" );
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document.write( "Suppose the interviewing office is on the left and the\r\n" );
document.write( "8 people are standing in line right to left waiting to\r\n" );
document.write( "be interviewed.\r\n" );
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document.write( "For illustrative purposes, take the arbitrary selected\r\n" );
document.write( "permutation DACDBBAC, written with a space after each,\r\n" );
document.write( "with the office on the left: \r\n" );
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document.write( "Office, D ,A ,C ,D ,B ,B ,A ,C\r\n" );
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document.write( "We can always fill the spaces with the subscripts 1 and 2, \r\n" );
document.write( "so that each letter with a 1 subscript is left of that same \r\n" );
document.write( "letter with a 2 subscript. That is, there is only 1 way to \r\n" );
document.write( "insert the subscripts in those spaces so that each mother \r\n" );
document.write( "stands in the line left of her daughter and therefore \r\n" );
document.write( "interviews before her daughter. That one way in this \r\n" );
document.write( "permutation is:\r\n" );
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document.write( "Office, D1 ,A1 ,C1 ,D2 ,B1 ,B2 ,A2 ,C2.\r\n" );
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document.write( "So the answer is the number of distinguishable permutations of\r\n" );
document.write( "AABBCCDD, which again is:\r\n" );
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document.write( "Edwin
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