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A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from, but only 5 flags will be flown.

Find the number of different signals consisting of 5 flags, if the first flag must be orange.

Answer :

Number of ways different signals of 5 color flags out 15 different colored flags with the condition of first flag must be orange is equal to 24024.

As given in the question,

Total number of different colored flags = 15

Number of flag to choose that will be flown = 5

Position of first flag is fixed by orange color

Rest four position will be filled by remaining 14 flags as all 5 flags are of different color

Required number of ways to form a signal of different color

= ¹⁴P₄

= (14!) / ( 14-4)!

= 14 × 13 × 12 × 11 × 10! / 10!

= 14 × 13 × 12 × 11

= 24024

Therefore, number of ways different signals of 5 color flags out 15 different colored flags with the condition of first flag must be orange is equal to 24024.

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