74. In the expression $(1+x)^{56}$, the parentheses are expanded and like terms are combined. Find the coefficients of $x^{8}$ and $x^{48}$,
74. Re-read the remark at the end of the solution to problem 71. Let's compare two expressions:

$$
(1+x)^{56} \text { and }\left(1+a_{1}\right)\left(1+a_{2}\right) \ldots\left(1+a_{55}\right) .
$$

If we set $a_{1}=a_{2}=\ldots=a_{56}=x$, then the second expression will turn into the first.

After expanding the brackets in the expression $\left(1+a_{1}\right)\left(1+a_{2}\right) \ldots\left(1+a_{56}\right) \quad$ there will be $C_{56}^{8}$ terms containing 8 letters. Any of these terms will turn into $x^{8}$ when each letter $a_{1}, a_{2}, \ldots, a_{56}$ is replaced by $x$.

Thus, the coefficient of $x^{8}$ in the expression $(1+x)^{56}$ (after expanding the brackets and combining like terms) is $C_{56}^{8}$.

Similarly, the coefficient of $x^{48}$ is $C_{56}^{48}$.

Remark. The numbers $C_{56}^{8}$ and $C_{56}^{48}$ are equal. Therefore, the coefficients of $x^{8}$ and $x^{48}$ in the expression $(1+x)^{56}$ are equal. Similarly, the coefficients of $x^{6}$ and $x^{30}$ in the expression $(1+x)^{56}$ are equal. Generally, in the expression $(1+x)^{n}$, the coefficients of $x^{k}$ and $x^{n-k}$ are equal; $C_{n}^{k}=C_{n}^{n-k}$.