Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Find the number of different signals consisting of nine flags that can be made using three white flags, five red flags and one blue flag

Sagot :

sqdancefan

Answer:

  504 possible signals

Step-by-step explanation:

If all of the flags are distinguishable, there are 9 choices for the first position, 8 for the second, 7 for the third, and on down to one final choice for the last position. The total number of choices is ...

  9·8·7·6·5·4·3·2·1 = 9! = 360,880

__

However, there are 3 white flags that are indistinguishable. Those three flags can be in any of 3·2·1 = 6 different orders, wherever they might be in the signal. Hence, we must divide the number of different signals by 6 to account for the indistinguishable white flags:

  362,880/6 = 60,480

Each of these signals has 5 red flags that are indistinguishable. Those can be in any of 5! = 120 different orders, wherever they are in the signal. Hence the total number of distinguishable signals is ...

  60480/120 = 504

504 different signals can be made from the 9 flags.

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.