Question 1210179
Let $M$ be the set of students who like Math, $E$ be the set of students who like English, and $H$ be the set of students who like History. We are given the following information:
\begin{itemize}
    \item $|M| = 68$
    \item $|E| = 85$
    \item $|H| = 55$
    \item $|M \cap E| = 20$
    \item $|M \cap H| = 15$
    \item $|E \cap H| = 22$
    \item $|M \cap E \cap H| = 8$
\end{itemize}
We want to find the number of students who like at least one subject, which is $|M \cup E \cup H|$. We can use the Principle of Inclusion-Exclusion to find this value:
$$|M \cup E \cup H| = |M| + |E| + |H| - |M \cap E| - |M \cap H| - |E \cap H| + |M \cap E \cap H|$$
Plugging in the given values, we get:
$$|M \cup E \cup H| = 68 + 85 + 55 - 20 - 15 - 22 + 8$$
$$|M \cup E \cup H| = 208 - 57 + 8$$
$$|M \cup E \cup H| = 151 + 8$$
$$|M \cup E \cup H| = 159$$
Thus, 159 students like at least one subject.

However, since there are only 150 students, this result is impossible. There must be an error in the given numbers. Let's recalculate:
$$|M \cup E \cup H| = 68 + 85 + 55 - 20 - 15 - 22 + 8$$
$$|M \cup E \cup H| = (68 + 85 + 55) - (20 + 15 + 22) + 8$$
$$|M \cup E \cup H| = 208 - 57 + 8$$
$$|M \cup E \cup H| = 151 + 8$$
$$|M \cup E \cup H| = 159$$

Let's verify the individual sets:
$|M \text{ only}| = |M| - |M \cap E| - |M \cap H| + |M \cap E \cap H| = 68 - 20 - 15 + 8 = 41$
$|E \text{ only}| = |E| - |M \cap E| - |E \cap H| + |M \cap E \cap H| = 85 - 20 - 22 + 8 = 51$
$|H \text{ only}| = |H| - |M \cap H| - |E \cap H| + |M \cap E \cap H| = 55 - 15 - 22 + 8 = 26$
$|M \cap E \text{ only}| = |M \cap E| - |M \cap E \cap H| = 20 - 8 = 12$
$|M \cap H \text{ only}| = |M \cap H| - |M \cap E \cap H| = 15 - 8 = 7$
$|E \cap H \text{ only}| = |E \cap H| - |M \cap E \cap H| = 22 - 8 = 14$
$|M \cap E \cap H| = 8$
$|M \cup E \cup H| = 41 + 51 + 26 + 12 + 7 + 14 + 8 = 159$

Since the result is 159, which is greater than the total number of students surveyed (150), there must be an error in the given data. However, assuming the given numbers are correct, the number of students who like at least one subject is 159.