Question 1167963
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          <U>(0)  The basic version</U>


The number of all possible outcomes is  10*10*10*10 = {{{10^4}}}.

It means that, in all,  {{{10^4}}} = 10000 tickets were issued.

So, the probability to win having one ticket is  P = {{{1/10^4}}} = {{{1/10000}}} = 0.0001.



          <U>version (i)</U>


The number of all possible outcomes is 10*9*8*7 = 5040.

It means that, in all,  5040 tickets were issued.

So, the probability to win having one ticket is  P = {{{1/(10*9*8*7)}}} = {{{1/5040}}}.



          <U>version (ii)</U>


The number of all possible outcomes is  {{{C[4]^2*10*9*8}}} = {{{((4*3)/2)*10*9*8}}} = 6*10*9*8 = 4320.

It means that, in all,  4320 tickets were issued.

So, the probability to win having one ticket is  P = {{{1/4320}}}.



          <U>Version (iii)</U>


The number of all possible outcomes is  {{{C[4]^2*10*9}}} = {{{((4*3)/2)*10*9}}} = 6*10*9 = 540.

It means that, in all,  540 tickets were issued.

Thus, the probability to win having one ticket is  P = {{{1/540}}}.
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Solved.