18. Argue that

$$ \binom{n}{n_1, n_2, ..., n_r} = \binom{n-1}{n_1-1, n_2,..., n_r} + \binom{n-1}{n_1, n_2-1,..., n_r} + ... + \binom{n-1}{n_1, n_2,..., n_r -1}$$

HINT: Use an argument similar to the one used to establish Equation (4.1).