document.write( "Question 1167755: Many states in U.S.A have a lottery game, usually called a Pick-4, in which you pick a fourdigit number such as 7359. During the lottery drawing, there are four bins, each containing balls
\n" ); document.write( "numbered 0 through 9. One ball is drawn from each bin to form the four-digit winning number.
\n" ); document.write( "a. You purchase one ticket with one four-digit number. What is the probability that you will
\n" ); document.write( "win this lottery game?
\n" ); document.write( "b. There are many variations of this game. The primary variation allows you to win if the four
\n" ); document.write( "digits in your number are selected in any order as long as they are the same four digits as
\n" ); document.write( "obtained by the lottery agency. For example, if you pick four digits making the number
\n" ); document.write( "1265, then you will win if 1265, 2615, 5216, 6521, and so forth, are drawn. The variations
\n" ); document.write( "of the lottery game depend on how many unique digits are in your number. Consider the
\n" ); document.write( "following four different versions of this game. Find the probability that you will win this
\n" ); document.write( "lottery in each of these four situations.
\n" ); document.write( "i. All four digits are unique (e.g., 1234)
\n" ); document.write( "ii. Exactly one of the digits appears twice (e.g., 1223 or 9095)
\n" ); document.write( "iii. Two digits each appear twice (e.g., 2121 or 5588)
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Algebra.Com's Answer #792374 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "(b, i)  In this case, you consider COMBINATIONS of 10 digits taken 4 at a time.\r\n" );
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document.write( "        There are   =  = 210  such combinations, in all.\r\n" );
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document.write( "        Of them, only one is winning.\r\n" );
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document.write( "        Therefore, the probability to win is    in this case.\r\n" );
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