How many different signals can be formed using 3 red, 2

Solution

We are given:

• 3 red flags
• 2 green flags
• 1 yellow flag

We are to find the number of different signals that can be formed using all these flags — where the order matters, but identical flags are indistinguishable. Total number of flags = 3 + 2 + 1 = 6 If all flags were distinct, the number of permutations = 6!=720 But since some flags are identical, we divide by factorials of repeated flags:

• 3 red flags ⇒ divide by 3!
• 2 green flags ⇒ divide by 2!
• 1 yellow flag ⇒ no need (1! = 1)

Total number of distinguishable signals: