Question

How many distinct signals can be made with 8 flags displayed at the same time in a vertical array if 3 flags are white, 2 flags are red, 1 flag is checkered and the rest of the flags are yellow?
1,680
3,360
6,720

Answer 1

Answer:

Option 1 -  1680 distinct signals can be made with 8 flags displayed at the same time in a vertical array.

Step-by-step explanation:

Given : 8 flags displayed at the same time in a vertical array if 3 flags are white, 2 flags are red, 1 flag is checkered and the rest of the flags are yellow.

To find : How many distinct signals can be made with 8 flags ?

Solution :        

The total number of flags is 8

White flag = 3

Red flag = 2

Checkered flag = 1

Yellow flag = 8-3-2-1=2

Applying the Fundamental Counting Principle which state that the multiplication of the events together to get the total number of outcomes.

The distinct signals can be made with 8 flags is

$T=\frac{8!}{3!\times 2!\times 1!\times 2!}$

$T=\frac{8\times 7\times 6\times 5\times 4\times 3!}{3!\times 2\times 1\times 1\times 2\times 1}$

$T=1680$

Therefore,Option 1 - 1680 distinct signals can be made with 8 flags displayed at the same time in a vertical array.

Answer 2

The answer is a. 
1,680 distinct signals can be made.