Liang has five balloons that are identical, except for their colour. Three are red (each labelled with an R) and two are green (each labelled with a G). He wants to put the five balloons in a row, but he is not sure which order he likes the best. How many different ways are there to arrange the five balloons in a row?

And please dont say some random answer or scam link.

Question

contestada

Respuesta :

joaobezerra joaobezerra · Answer 1 · 2022-03-17T10:35:46+01:00

Using the arrangements formula, it is found that there are 10 different ways to arrange the five balloons in a row.

The number of possible arrangements of n elements is the factorial of n, that is:

[tex]A_n = n![/tex]

When elements repeat [tex]n_1, n_2, \cdots n_n[/tex] times, we have that:

[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In this problem, 5 elements, repeating 3 and 2 times, hence:

[tex]A_5^{3,2} = \frac{5!}{3!2!} = 10[/tex]

There are 10 different ways to arrange the five balloons in a row.

More can be learned about the arrangements formula at https://brainly.com/question/24648661