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

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

Answer 2

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

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=(8!)/(3!* 2!* 1!* 2!)`

`T=(8* 7* 6* 5* 4* 3!)/(3!* 2* 1* 1* 2* 1)`

`T=1680`

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