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PERMUTATIONS AND COMBINATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPERMUTATIONS AND COMBINATIONS1 Mark
MCQ
How many different signals can be transmitted by arranging 3 red, 2 yellow and 2 green flags on a pole: [Assume that all the 7 flags are used to transmit a signal].
  • ✓
    210
  • B
    215
  • C
    220
  • D
    225
✓

Answer

Correct option: A.
210
Here, $\text{n}=3+2+2=7$
$\text{P}_1=3,\text{P}_2=2$ and $\text{P}_3=2$
$\therefore$ Required number of different signals
$=\frac{\text{n}!}{\text{p}_1!\text{p}_1\text{p}_1}=\frac{7!}{3!2!1!}=\frac{7.6.5.4}{2.2}$
$=7.6.5=210$

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