A ship carries exactly 10 different signal flags. If each
possible combination and ordering of 4 of these flags
connotes a specific message, how many signals can be
sent with these flags, taken 4 at a time?
To find the number of signals that can be sent with these flags taken 4 at a time, we can use the concept of combinations.
In this case, we have 10 different flags and we need to select 4 of them at a time. The order in which we select the flags does not matter. The formula to calculate the number of combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n represents the total number of items and r represents the number of items selected.
Using this formula, we can calculate the number of signals:
C(10, 4) = 10! / (4! * (10 - 4)!)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210
Therefore, there can be 210 different signals that can be sent with these flags, taken 4 at a time.