Chapter 13, Problem 20RE

Arranging Flags How many different vertical arrangements are there of 10 flags if 4 are white, 3 are blue, 2 are green, and 1 is red?

To determine

To find: How many different vertical arrangements are there of 10 flags?

Answer to Problem 20RE

12600 arrangements.

Explanation of Solution

Given:

Of 10 flags, 4 are white, 3 are blue, 2 are green, and 1 is red.

Formula used:

The number of permutation of n objects that are not distinct is $\frac{n!}{n_1 ! n_2 ! n_3 ! \dots \mathrm{..}{n}_k !}$ where $n_1, n_2\dots \mathrm{..}{n}_k$ each are of different kind.

Calculation:

Of 10 flags, 4 are white, 3 are blue, 2 are green, and 1 is red.

$n_1 = 4$, $n_2 = 3$, $n_3 = 2$ and $n_4 = 1$; $n = 4 + 3 + 2 + 1 = 10$

The number of different vertical arrangements are $\frac{10 ! }{4 ! 3 ! 2 ! 1 !} = 12600$.

12600 different vertical arrangements are there of 10 flags.