The number of multisets of length on
symbols is sometimes termed " multichoose ," denoted by analogy with the binomial
coefficient .
multichoose is given by the simple formula

where
is a multinomial coefficient. For example,
3 multichoose 2 is given by 6, since the possible multisets of length 2 on three
elements
are , , , , , and .

The first few values of
are given in the following table.

1

2

3

4

5

1

1

2

3

4

5

2

1

3

6

10

15

3

1

4

10

20

35

4

1

5

15

35

70

5

1

6

21

56

126

Multichoose problems are sometimes called "bars and stars" problems. For example, suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility
is an arrangement of 5 spices (stars) and dividers between categories (bars), where the notation indicates a choice of spices
1, 1, 5, 6, and 9 (Feller 1968, p. 36). The number of possibilities in this
case is then ,