Question

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?

Short answer

$12,600$different arrangements.

Step-by-step solution

Step 1. Given information.

$10$flags are given.

In which $4$are white, $3$are blues,$2$are green and$1$is red.

Step 2. Calculation.

We seek the number of permutations of $8$objects of which role="math" localid="1647416956508" $4,3,2,1$are different kinds of color.

We use formula-

$$\begin{gathered} \frac{10!}{4!3!2!1!}=\frac{10\times 9\times 8\times 7\times 6\times 5\times 4!}{4!3!2!1!} \\ =\frac{10\times 9\times 8\times 7\times 6\times 5}{3\times 2\times 2} \\ =12,600 \end{gathered}$$