document.write( "Question 1164753: a) In how many different ways can the letters of the word KNOWLEDGE be
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Algebra.Com's Answer #789168 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Yes, she's right.  I didn't count the \"G\".  I fixed it below:\r\n" );
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document.write( "a)	In how many different ways can the letters of the word KNOWLEDGE be\r\n" );
document.write( "arranged in such a way that the vowels always come together?\r\n" );
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document.write( "We can choose the 3 vowels to be together (call it a \"vowel trio\") any of\r\n" );
document.write( "these 3 ways: EEO, EOE, OEE.\r\n" );
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document.write( "For each of those 3 choices, there are 7 things (six single letters and one\r\n" );
document.write( "vowel-trio).  The 7 things are\r\n" );
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document.write( "K, N, W, L, D, G, (the vowel trio)\r\n" );
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document.write( "There are 7! ways to arrange those six things:\r\n" );
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document.write( "Answer: 3∙7! = 3∙5040 = 15120 ways.\r\n" );
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b) In a group of 6 boys and 4 girls, four children are to be selected. In
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document.write( "how many different ways can they be selected such that at least one boy
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document.write( "should be there?
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document.write( "If we didn't care whether there was at least one boy the answer would be\r\n" );
document.write( "10 children choose 4 = C(10,4) or 10C4 = 210 ways.\r\n" );
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document.write( "There is just 1 unwanted situation, when the four girls are chosen.  That's\r\n" );
document.write( "because we can choose all girls in just one way. C(4,4) or 4C4 = 1.  So we\r\n" );
document.write( "just need to subtract 1 for that 1 unwanted situation:\r\n" );
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document.write( "Answer: 210-1 = 209 ways.\r\n" );
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document.write( "Edwin
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