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How many different signals can be transmitted by hoisting 3 red, 4 yel

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Bunuel
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How many different signals can be transmitted by hoisting 3 red, 4 yel [#permalink] New post   04 Jan 2021, 01:14
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How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?

A. 1260
B. 1080
C. 960
D. 880
E. 720
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Re: How many different signals can be transmitted by hoisting 3 red, 4 yel [#permalink] New post   04 Jan 2021, 01:29
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\(\frac{9!}{3!*4!*2!}=9*4*7*5=1260\)

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Re: How many different signals can be transmitted by hoisting 3 red, 4 yel [#permalink] New post   04 Jan 2021, 19:27
since all 9 flags need to be used in order to produce a signal, the flags could be used in many ways.

RRRBBYYYY
RBBYYRYYR
.
.
.
.
.
.
and so on,

Thus, the number of ways is: 9!/(2!*3!*4!) = 1260 = A

Please let me know if you have questions :)

Kudos if you like my solution :)
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Re: How many different signals can be transmitted by hoisting 3 red, 4 yel [#permalink] New post   06 Mar 2021, 10:38
Bunuel wrote:
How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?

A. 1260
B. 1080
C. 960
D. 880
E. 720

\(R_1 = R_2 = R_3 = R\)
\(Y_1 = Y_2 = Y_3 = Y_4 = Y\)
\(B_1 = B_2 = B\)

In reality there are 9! ways to arrange the different signals but since every red color flag would give a same signal. Hence position of any one of the 3 red flags would be same as to be held by 2nd or 3rd red flag.
This would be same for yellow as well as blue flag.

Hence unique ways of arrangements of flags = \(\frac{9!}{3!*4!*2!} = 1260\)

Answer A.
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Re: How many different signals can be transmitted by hoisting 3 red, 4 yel [#permalink]
06 Mar 2021, 10:38
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