Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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.

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.