Question

Jeanine baker makes floral arrangements. She has 18 different cut flowers and plans to use 6 of them. How many different selections of the 6 flowers are possible?

Answer 1

Considering the definition of combination, 18,564 different selections of the 6 flowers are possible.

Definition of combination

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.

To calculate the number of combinations, the following formula is applied:

$C=\frac{m!}{n!(m-n)!}$

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

Different selections of the flowers

Jeanine baker makes floral arrangements. She has 18 different cut flowers and plans to use 6 of them. Then, you know that:

• m= 18
• n= 6

Replacing in the definition of combination:

$C=\frac{18!}{6!(18-6)!}$

Solving:

$C=\frac{18!}{6!12!}$

C= 18,564

Finally, 18,564 different selections of the 6 flowers are possible.

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