Question

# How many different signals can be made by $5$flags from $8$flags of different colors?

A

$10$

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B

$6720$

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C

$20$

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D

None of these

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Solution

## The correct option is B $6720$Find the number of different signals :Here we have to arrange $8$flags taken $5$flags at a time which is equivalent to filling $8$flags placed out of $5$flags. For that, we have the formula of permutation:${}^{\mathbf{n}}\mathbit{P}_{\mathbf{r}}$.Number of different signals made by $5$ flags from $8$ different colored flags $={}^{8}P_{5}$$=\frac{8!}{\left(8-5\right)!}=\frac{8!}{3!}=8×7×6×5×4=6720$Therefore the required number of signals can be made by $5$flags from $8$flags of different colors is $6720$.Hence, the correct option is B.

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