Discrete Mathematics

228

DISCRETE

MATHEMATICS·-------------------------

we call the children

1,

2,

.... ,

k;

thus we are given the numbers (non-negative integers) n

1

, n

2

, ..

..

,nk. We assume

that

n

1

+ n

2

+

....

+

nk

= n, else there is no way to distribute the presents.

The question is,

of

course, in how many ways can these presents be distributed?

We

can organize the

distribution

of

presents as follows. We lay out the presents in a single row

of

length

n.

The ftrst child comes

and picks up the ftrst n

1

presents, starting from the left. Then the second comes and picks up the next n

2

;

then

the third picks up the next

n

3

presents and so on. The

JCb

child gets the