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Number different secret messag signal: Rectangular Aags' of various solid colors (but not necessarily of the game size) are arranged on vertical pole: Flags of...

Question

Number different secret messag signal: Rectangular Aags' of various solid colors (but not necessarily of the game size) are arranged on vertical pole: Flags of the game size and color are indietinguishable from one another: Each distinguishable arrangement ofall-the Auge" on the pole Is different signal: In this question we are interested-in - counting the_number of signals poesiblein various situations. Suppose there flags: red, black and green_ In parts &) to d) below, count how

number different secret messag signal: Rectangular Aags' of various solid colors (but not necessarily of the game size) are arranged on vertical pole: Flags of the game size and color are indietinguishable from one another: Each distinguishable arrangement ofall-the Auge" on the pole Is different signal: In this question we are interested-in - counting the_number of signals poesiblein various situations. Suppose there flags: red, black and green_ In parts &) to d) below, count how many signals are poBsible: Express your answers in terms of factorials Remember, the only restrictions are the stated ones: Flags = of the game color have noticeably different gize (say 8mall, medium and large). Ly fags heve the same ;ize- 842 3 37 All flags heve the game gize and thoge of the same color grouped together _ d) Flags of the game color have noticeably different gize, and those of the same color grouped together: they are randomly arranged on the pole; then what is the probability If flegs all have the same size and Garvey" fleg " (from top to bottom: red_ black and green)? that the colors form the Marcus



Answers

Tell whether each situation is a permutation or combination. How many different flags can be made from the colors red, blue, green, and white if each flag has three vertical stripes?

A flag signal consists of seven Flags that they're hung vertically. If you have three identical red flags, toe identical blue flags and two identical white flags. How many different flags signals can be made for this problem? We're going to use permutation Rule number two, which basically states that the number of permutations off any objects where are one objects are identical are two objects are identical, and so on are be objects are identical is given by the formula in factorial over our one factorial are two factorial time Central on R B Factorial, in this case are one place are too blush, and John R B should equal to end. So if we apply it to our problem, seven flags in the flag signals a seven factorial divided by three factorial for the red flags, which are identical times. Two factorial for the two blue identical flags. Times two factorial for the white identical flags. And that should equal using your calculator that would be equal to 210 different flags signals

All right, so we have five flags and we're gonna host up three of them. So that's five. Choose three. That means we have five factorial over five minus three factorial, which is two factorial, which means that anything from two down is gonna cancel out. So we just have five times. Four times three, which is 60.

We are given that the ship GoDaddy's fine signal flags, each off different color on were asked how many different signals can be said by hosting exactly three flags. That means the number of signals combined by flags are gonna be equal to three out off five flags that I used. So that is five Wheatley, which is equal to three times four times five. That's 60 ways or 60 signals that can be created.

For this question, we have a shift that it's five different signal flies off five different colors. We're supposed to find out the number of different ways in which we can hoist three out of the five flags to send a signal. Now, since we have five flags, we have five choices for the first flag. Now, after you have the first leg chosen, we have four choices for the second one. And after choosing the first two, flags were left with three flags to choose from. So we have three choices for the total. Now the number of different ways you could arrange. This is five times four banks three, which is 60 now. Another way to look at this is we're basically filling in three places out of the fight. So that's permutations off three out of five. We know that this comes to five factorial divided by five minus trees Sectorial. This is basically five factorial divided by two factorial. Five factorial is 1 20 two. Factorial is too. So the final answer we get is 60 again. So 60 here is our final answer


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