document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202488>Question 202488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone PLEASE help me with these? Thank You. :)\r<BR>\n" );
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document.write( "1) A person is wearing a bracelet with 11 settings around the bracelet. How many different ways can 11 birthstones be arranged around the bracelet? Leave the answer in factorial form.\r<BR>\n" );
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document.write( "2) How many subsets of four elements each exist in a set of seven elements?<BR>\n" );
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document.write( "3) How many different groups of 35 cars can be formed from 40 cars?<BR>\n" );
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document.write( "4) How many different ways can an executive committee of nine people sit at a round table?\r<BR>\n" );
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document.write( "5) What is the probability of not drawing a green marble from a jar containing 7 red, 4 green, 3 white, and 9 blue marbles?\r<BR>\n" );
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document.write( "6) A compound experiment consists of drawing at random twice without replacing from a jar with 3 red, 3 white, and 2 black marbles. What is the probability of getting first a red and then a black marble?\r<BR>\n" );
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document.write( "Thanks again,<BR>\n" );
document.write( "~Sarah </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152724 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> permutations are an ordered set.  each set can contain the same elements as another set only in a different order.<BR>\n" );
document.write( "the formula for permutations is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-x%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-x%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "combinations are an unordered set.  each set cannot contain the same elements as another set regardless of the order.<BR>\n" );
document.write( "the formula for combinations is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28%28n-x%29%21%2Ax%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28%28n-x%29%21%2Ax%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a simple example:<BR>\n" );
document.write( "letters abc.<BR>\n" );
document.write( "sets of 2 letters<BR>\n" );
document.write( "permutations would be: ab, ba, ac, ca, bc, cb.<BR>\n" );
document.write( "formula for permutations would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%21%2F1%21 ALIGN=MIDDLE  ALT=\"3%21%2F1%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6<BR>\n" );
document.write( "note that 1! was the result of (3-2)! which = 1!.<BR>\n" );
document.write( "combinations would be: ab, ac, bc<BR>\n" );
document.write( "formula for combinations would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%21%2F%281%21%2A2%21%29 ALIGN=MIDDLE  ALT=\"3%21%2F%281%21%2A2%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your problems:<BR>\n" );
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document.write( "1) A person is wearing a bracelet with 11 settings around the bracelet. How many different ways can 11 birthstones be arranged around the bracelet? Leave the answer in factorial form.<BR>\n" );
document.write( "we're looking for permutations here.<BR>\n" );
document.write( "the formula should be how many permutations of 11 can you get out of a set of 11.<BR>\n" );
document.write( "the formula should be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-x%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-x%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where:<BR>\n" );
document.write( "n = 11 = set you are drawing from.<BR>\n" );
document.write( "x = 11 = set you want to create.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%21%2F%2811-11%29%21 ALIGN=MIDDLE  ALT=\"11%21%2F%2811-11%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%21%2F0%21 ALIGN=MIDDLE  ALT=\"11%21%2F0%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%21%2F1 ALIGN=MIDDLE  ALT=\"11%21%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%21 ALIGN=MIDDLE  ALT=\"11%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "please note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%21 ALIGN=MIDDLE  ALT=\"0%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.  <BR>\n" );
document.write( "this may be counter-intuitive but it is correct.  if you want to see a decent explanation, go to this website and look at the best answer to the question.<BR>\n" );
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document.write( "http://answers.yahoo.com/question/index;_ylt=AsdGQIzGmbF_exSCD_gWWxYjzKIX;_ylv=3?qid=20060811004831AAT49h4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "anyway, back to your problem.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%21 ALIGN=MIDDLE  ALT=\"11%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 11*10*9*8*7*6*5*4*3*2*1 = 39,916,800 possible ways the birthstones can be arranged on the necklace.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if it was 2 beads they could be arranged <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%21 ALIGN=MIDDLE  ALT=\"2%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways = 2*1 = 2 ways<BR>\n" );
document.write( "if it was 3 beads they could be arranged <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%21 ALIGN=MIDDLE  ALT=\"3%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways = 3*2*1 = 6 ways<BR>\n" );
document.write( "if it was 4 beads they could be arranged <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%21 ALIGN=MIDDLE  ALT=\"4%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways = 4*3*2*1 = 24 ways<BR>\n" );
document.write( "you can see as the number of beads gets larger, the possible permutations (these are permutations because they contain the same beads only in a different order) becomes much larger.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "2) How many subsets of four elements each exist in a set of seven elements?<BR>\n" );
document.write( "looks like they want combinations here since order is not important.<BR>\n" );
document.write( "n = 7<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "formula for number of combinations is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28%28n-x%29%21%2Ax%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28%28n-x%29%21%2Ax%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this winds up being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%21%2F%28%287-4%29%21%2A%284%21%29%29 ALIGN=MIDDLE  ALT=\"7%21%2F%28%287-4%29%21%2A%284%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%21%2F%283%21%2A4%21%29 ALIGN=MIDDLE  ALT=\"7%21%2F%283%21%2A4%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "7*6*5*4*3*2*1/1*2*3*1*2*3*4<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "35<BR>\n" );
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document.write( "The possible number of subsets = 35.<BR>\n" );
document.write( "Each subset will not contain the same elements as any other subset.<BR>\n" );
document.write( "Order is not important.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "3) How many different groups of 35 cars can be formed from 40 cars?<BR>\n" );
document.write( "this looks like combinations again, since different groups would not contain the same cars in each group in a different order.<BR>\n" );
document.write( "formula would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840%29%21%2F%28%2840-35%29%21%2A%2835%29%21%29 ALIGN=MIDDLE  ALT=\"%2840%29%21%2F%28%2840-35%29%21%2A%2835%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840%2A39%2A38%2A37%2A36%2A35%21%29%2F%2835%21%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2840%2A39%2A38%2A37%2A36%2A35%21%29%2F%2835%21%2A5%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which equals 658008<BR>\n" );
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document.write( "4) How many different ways can an executive committee of nine people sit at a round table? <BR>\n" );
document.write( "This should be permutations again.<BR>\n" );
document.write( "It is similar to the beads question but only this time we have 9 executives instead of 11 beads.<BR>\n" );
document.write( "Your answer should be 9! = 9*8*7*6*5*4*3*2*1 = 362,880.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "5) What is the probability of not drawing a green marble from a jar containing 7 red, 4 green, 3 white, and 9 blue marbles? <BR>\n" );
document.write( "there are 4 green marbles in the set.<BR>\n" );
document.write( "the probability of not drawing a green marble should be 1 - the probably of drawing a green marble.<BR>\n" );
document.write( "the total marbles in the set are 7+4+3+9 = 23.<BR>\n" );
document.write( "since there are 4 marbles in the set, the probability of drawing a green marble is 4/23.<BR>\n" );
document.write( "therefore, the probability of not drawing a green marble should be 1 - 4/23 = 19/23.<BR>\n" );
document.write( "another way of looking at it is:<BR>\n" );
document.write( "the probability of not drawing a green marble is the probability of drawing any marble that is not green.<BR>\n" );
document.write( "out of the 23 marbles, 19 of them are not green (7 red + 3 white + 9 blue), so the probability of drawing a marble that is not green is 19/23.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "6) A compound experiment consists of drawing at random twice without replacing from a jar with 3 red, 3 white, and 2 black marbles. What is the probability of getting first a red and then a black marble? <BR>\n" );
document.write( "you start off with 3 red 3 white 2 black marlbes for a total of 8 marbles.<BR>\n" );
document.write( "on your first draw, the probability of drawing a red marble is 3/8.<BR>\n" );
document.write( "assuming you got the red marble you were looking for, then the probability of getting a black marble on the second draw is 2/7.  the reason for this is that you got the red marble on the first draw and didn't return it into the pot so what was left was 2 red 3 white 2 black marbles.<BR>\n" );
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document.write( "now, the probability of event A happening and then event B happening is the p(A) * p(B) which means that the probability of first getting a red and then getting a black would be 3/8 * 2/7 = 6/56.<BR>\n" );
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document.write( "you can look at that as follows:  3/8 of the time you get a red.  within that 3/8 of the time, 2/7 of the time you get a black on the second draw.<BR>\n" );
document.write( "getting them both can only happen 3/8 * 2/7 of the time.<BR>\n" );
document.write( "try smaller number again to see what's happening.<BR>\n" );
document.write( "you have a pot with 3 letters in it.<BR>\n" );
document.write( "a,b,c<BR>\n" );
document.write( "what is the probability of getting an (a) and then a (b)?<BR>\n" );
document.write( "you will get the (a) 1/3 of the time.<BR>\n" );
document.write( "once you get the (a), you will get the (b) 1/2 of the time, assuming you didn't return the (a) into the pile.<BR>\n" );
document.write( "the possible combinations in order of how they were drawn is as follows:<BR>\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ba<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "ca<BR>\n" );
document.write( "cb<BR>\n" );
document.write( "the only successful draw would be ab which represents 1/6 of the total possible combinations.<BR>\n" );
document.write( "1/3 * 1/2 = 1/6 so the formula of p(a) * p(b) is good and the answer for this example is 1/6.  <BR>\n" );
document.write( "It is not, however, the answer to the last question.  It is only the answer to the example I just used.<BR>\n" );
document.write( "the answer to your last question is 6/56 as I indicated above. </SPAN>\n" );
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