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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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