Let $N = \{1,2,3,4,5,6,7,8,9\}$ and $L = \{a,b,c\}$. Statements (29) Suppose we arrange the 12 elements of $L \cup N$ in a line such that all three letters appear consecutively (in any order). The number of such arrangements is less than $10! \times 5$. (30) More than half of the functions from $N$ to $L$ have the element $b$ in their range. (31) The number of one-to-one functions from $L$ to $N$ is less than 512. (32) The number of functions from $N$ to $L$ that do not map consecutive numbers to consecutive letters is greater than 512. (e.g., $f(1) = b$ and $f(2) = a$ or $c$ is not allowed. $f(1) = a$ and $f(2) = c$ is allowed. So is $f(1) = f(2)$.)
Let $N = \{1,2,3,4,5,6,7,8,9\}$ and $L = \{a,b,c\}$.
Statements
(29) Suppose we arrange the 12 elements of $L \cup N$ in a line such that all three letters appear consecutively (in any order). The number of such arrangements is less than $10! \times 5$.\\
(30) More than half of the functions from $N$ to $L$ have the element $b$ in their range.\\
(31) The number of one-to-one functions from $L$ to $N$ is less than 512.\\
(32) The number of functions from $N$ to $L$ that do not map consecutive numbers to consecutive letters is greater than 512. (e.g., $f(1) = b$ and $f(2) = a$ or $c$ is not allowed. $f(1) = a$ and $f(2) = c$ is allowed. So is $f(1) = f(2)$.)