Using the combination formula, it is found that if the first flag is orange then the number of different signals consisting of 4 flags is 364.
The order in which the flags are chosen is not important, hence, the combination formula is used to solve this question.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, considering that the first flag is orange, 3 flags will be chosen from a set of the remaining 14, hence the number of signals is given by:
[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
