# 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?
$\left(4!×5!×8!\right)×3!$
$480$
$\left(4!×5!×8!\right)÷3!$
${\left(160\right)}^{3}$
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?
${\left(5!\right)}^{2}$
${\left(5!\right)}^{2}×10!×2!$
$10!$
$25$
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?
$18$
$2!×9!$
${9}^{2}$
${2}^{9}$
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?
$16$
$64$
$992$
$32!$
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.
$15$
$720$
$5040$
$42$
Question 6:   There are $\text{\hspace{0.17em}}15\text{\hspace{0.17em}}$ men working for security service. It is needed to organize protection of two buildings with three and four floors (one man on each floor). In how many ways it can be organized?
$105$
${C}_{15}^{3}×{C}_{12}^{4}$
$15!$
${A}_{15}^{3}×{A}_{12}^{4}$
Question 7:   Mother has $\text{\hspace{0.17em}}9\text{\hspace{0.17em}}$ candies. In how many ways she can give these candies to her $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ children so that each gets $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ candies?
$27$
${A}_{9}^{3}×{A}_{6}^{3}$
$729$
$1680$
Question 8:   There are $\text{\hspace{0.17em}}12\text{\hspace{0.17em}}$ girls and $\text{\hspace{0.17em}}15\text{\hspace{0.17em}}$ boys in the class. In how many ways four pairs for a school dance can be chosen out of them? (A pair means boy-girl pair)
${12}^{4}$
$720$
${C}_{12}^{4}×{C}_{15}^{4}×4!$
${C}_{12}^{4}×{C}_{15}^{4}$
Question 9:   The coin is being tossed by two times. What is the probability of tails coming up both times?
$0.1$
$0.25$
$0.5$
$0$
Question 10:   In a $\text{\hspace{0.17em}}36$ -card deck there are $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ suits, $\text{\hspace{0.17em}}9\text{\hspace{0.17em}}$ cards in each. What is the probability when after dealing cards to four players (each gets nine cards), everyone gets cards of the same suit?
${9}^{4}$
$\frac{4!×9!×9!×9!×9!}{36!}$
$36!$
${36}^{2}$