# Test: Probability I - Challenging

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Question 1:   A student has $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ math books, $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ English books and $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ history books. In how many ways can this student put the books on the shelf so that books of the same subject would stand together?
$480$
$\left(4!×5!×8!\right)×3!$
${\left(160\right)}^{3}$
$\left(4!×5!×8!\right)÷3!$
Question 2:   Five girls and five boys are sitting down on $\text{\hspace{0.17em}}10\text{\hspace{0.17em}}$ chairs one after one. In how many ways they can sit so that boys would sit on the chairs with even numbers and girls - in the chairs with odd numbers?
$25$
$10!$
${\left(5!\right)}^{2}$
${\left(5!\right)}^{2}×10!×2!$
Question 3:   In how many ways can the orders of printing $\text{\hspace{0.17em}}9\text{\hspace{0.17em}}$ different books be distributed to $\text{\hspace{0.17em}}2\text{\hspace{0.17em}}$ factories?
$18$
${9}^{2}$
${2}^{9}$
$2!×9!$
Question 4:   There are $\text{\hspace{0.17em}}32\text{\hspace{0.17em}}$ students in a classroom. Each second student exchanged a pen for another one. How many times pens were exchanged?
$992$
$16$
$64$
$32!$
Question 5:   How many different six-digit numbers can be formed out of $\text{\hspace{0.17em}}1,2,3,4,5,6,7\text{\hspace{0.17em}}$?  Digits should not repeat and only even digits should be at the beginning and the end of a number.
$5040$
$42$
$15$
$720$
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