Question 1127127
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To solve the problem  (and to understand the solution),  you need to be familiar with permutations.


Are you familiar with it ?


If not,  look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Problems on Permutations</A>

in this site.


For example, &nbsp;to answer &nbsp;a), &nbsp;you need to know &nbsp;that there are  &nbsp;&nbsp;10! = 10*9*8*7*6*5*4*3*2*1  &nbsp;permutations of &nbsp;10 objects,  
and only one of them is the identical permutation.


In other words, &nbsp;there are &nbsp;10! = 10*9*8*7*6*5*4*3*2*1 &nbsp;possible outcomes in this game, &nbsp;and only one of them is favorable.


It gives the answer for &nbsp;a):  &nbsp;&nbsp;Probability = {{{1/10!}}} = {{{1/3628800}}} = {{{2.7557*10^(-7)}}}.


Notice that your answer for &nbsp;a) &nbsp;is written &nbsp;INCORRECTLY.


The answer for b), &nbsp;which you printed in your post, &nbsp;is incorrect, too.