$1: 36$ Find the number of combinations of $k$ different elements $\left(j_{1}, j_{2}, \cdots, j_{k}\right)$ taken from $\{1,2, \cdots, n\}$ that satisfy the following conditions:
(1) $1 \leqslant j_{1}<j_{2}<\cdots<j_{k} \leqslant n$;
(2) $j_{i}-j_{i-1} \geqslant m, i=2,3, \cdots, k, m \in N$.
［Solution］Let
$$
j_{i}^{\prime}=j_{i}-(i-1)(m-1), i=1,2, \cdots, k,
$$

Then by (2) we know
$$
j^{\prime}{ }_{i+1}-j^{\prime}{ }_{i}=j_{i+1}-j_{i}-(m-1) \geqslant 1, i=1,2, \cdots, k-1 .
$$

Also by (1) we have
$$
1 \leqslant j^{\prime}{ }_{1}<j^{\prime}{ }_{2}<\cdots<j^{\prime}{ }_{k} \leqslant n-(k-1)(m-1) .
$$

It is easy to see that this correspondence is a bijection. Therefore, the required combination number is $C_{n-(k-1)(m-1)}^{k}$.