Question

Joseph is planning dinners for the next 4 nights. There are 10 meals to choose from. If no meal is repeated, how many different meal arrangements are possible?

Answer 1

Considering the definition of combination, if no meal is repeated, 210 different meal arrangements are possible.

What is 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:

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

The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.

Different meal arrangements

Joseph is planning dinners for the next 4 nights. There are 10 meals to choose from and no meal is repeated.

So, you know that:

• m= 10
• n= 4

Replacing in the definition of combination:

$C=\frac{10!}{4!(10-4)!}$

Solving:

$C=\frac{10!}{4!6!}$

$C=\frac{3,628,800}{24x720}$

$C=\frac{3,628,800}{17,280}$

C= 210

Finally, if no meal is repeated, 210 different meal arrangements are possible.

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