Question

What is the number of different signals that can be formed from the following set of flags: 4 red flags, 3 white flags, and a blue flag, knowing that each signal consists of 8 flags arranged vertically?​

Answer 1

Explanation:

Given :-

Total number of flags hung in a vertical line = 8

white flags = 2 .

Red flags = 3 .

Blue flags = 3 .

To Find :-

How many different signals can be made ?

Solution :-

→ Total different signals made = (Total number of flags hung)! / [(white flags)! * (Red flags)! * (Blue flags)!]

putting given values we get,

→ Total different signals made = 8!/(2! * 3! * 3!)

→ Total different signals made = (8 * 7 * 6 * 5 * 4 * 3!) / (2! * 3! * 3!)

→ Total different signals made = (8 * 7 * 6 * 5 * 4) / (2 * 3 * 2)

→ Total different signals made = (8 * 7 * 6 * 5 * 4) / (6 * 2)

→ Total different signals made = (8 * 7 * 5 * 4) / 2

→ Total different signals made = 8 * 7 * 5 * 2

→ Total different signals made = 560 (Ans.)