How many different signals using 6 flags can be made if 3 are red, 2 are blue and 1 is white
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A signal has $6$ flags, each flag can be blue, white or red. Possible signals formed is $n^r = 3^6 = 729$ possible signals formed How many different signal can be made from $6$ flags of which $3$ are white, $2$ are red and $1$ is blue? Order does matter - so permutation is this a case of $3! \cdot 2! \cdot 1!$ so $6 \cdot 2 \cdot 1 = 12$ ways? I'm not sure if this is right ...
asked Oct 9, 2014 at 22:33
$\endgroup$ $\begingroup$ Out of the six flags, there are $\binom{6}{3} = 20$ ways to choose which flags are going to be white. Now out of the remaining three flags, pick which one is going to be blue, and the remaining two will automatically be red. answered Oct 9, 2014 at 22:44
$\endgroup$ $\begingroup$ The number of choices for the blue flag is $6$. For each of these choices, there are $$\binom{5}{2}$$ ways to choose the two red flags of the remaining five flags. The last three flags have to be white. This gives a final answer of $$6 \cdot \binom{5}{2} = 6 \cdot \frac{5\cdot 4}{2} = \boxed{60}$$ answered Oct 9, 2014 at 22:45
Zubin MukerjeeZubin Mukerjee 17.3k3 gold badges33 silver badges74 bronze badges $\endgroup$ $\begingroup$ First place the $3$ whites so that is $6 \choose 3$. Out of the $3$ remaining spots, place the $2$ reds so that is $3 \choose 2$. There is only $1$ remaining spot for the blue. So the answer is $6 \choose 3$ * $3 \choose 2$ * $1$ = $60$. answered Oct 10, 2014 at 1:21
DavidDavid 1,6741 gold badge22 silver badges40 bronze badges $\endgroup$ How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff? Nội dung chính
Advertisement Remove all ads SolutionWe have to arrange 9 flags, out of which 4 are of one kind (red), 2 are of another kind (white) and 3 are of the third kind (green). Concept: Factorial N (N!) Permutations and Combinations Is there an error in this question or solution? Advertisement Remove all ads Chapter 16: Permutations - Exercise 16.5 [Page 43] Q 8Q 7Q 9 APPEARS INRD Sharma Class 11 Mathematics Textbook Chapter 16 Permutations Advertisement Remove all ads How many signals can 4 flags of different colors using two flags at a time?Hence we have the total number of signals possible is 12. How many signals can be made by arranging 9 flags in a line if 4 are Red 3 are blue and 2 are white?Thus, 1260 different signals can be made. How many different 3 flag signals are there?So, we can say that the total possible ways to signal using 3 different flags can be calculated by adding total ways to signal by individual flags (1 at a time + 2 at a time + all 3 at a time). So, there are a total of 15 different ways. Hence, option (C) is correct. How many different signals each consisting of 6 flags hung in a vertical line can be formed from 4 identical red flags and 2 identical green flags?From the given, we know that n=6 . We can set r1=4 r 1 = 4 , which corresponds to the 4 identical red flags, and r2=2 r 2 = 2 , which corresponds to 2 identical blue flags. We will plug these values into the formula. Therefore, we can make 15 different signals from the set of flags. How many signals does Six flags make?Number of signals using one flag = 6P1 = 6Number of signals using two flags = 6P2 = 30Number of signals using three flags = 6P3 = 120Number of signals using four flags = 6P4 = 360Number of signals using five flags = 6P5 = 720Number of signals using all six flags = 6P6 = 720Therefore the total number of signals using ...
How many different 3 flag signals are there?So, we can say that the total possible ways to signal using 3 different flags can be calculated by adding total ways to signal by individual flags (1 at a time + 2 at a time + all 3 at a time). So, there are a total of 15 different ways. Hence, option (C) is correct.
How many different signals can be made from 4 red 2 white and 3 green flags by arranging all them vertically on a Flagstaff ?Hence, total number of signals = 1260.
How many different signals are possible with 4 blue 3 red 2 white and 2green flags by using all at a time in a queue?Total 69300 different signals are possible with 4 blue, 3 red, 2 white and 2 green flags by using all at a time in a queue.
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