A signal lac has six flags of which 1is blue ,two z white,3 ar red.it sends messages hostin flags in a flagpole.d messages ar being conveyed by d order in which d colours ar arranged find hw many mesaages it can send.......a.using exactly six flags,b.using exactly five flags

your economy of typing (laziness?) makes your posting almost unintelligible.

We don't mind helping you find the answers, but don't ask us to figure out the questions as well, ok?

and what the heck is a signal lac?

To find the number of messages that can be sent using the given flags, we need to consider the different permutations of the colors.

a. Using exactly six flags:
Since there are 1 blue, 2 white, and 3 red flags, we can arrange them in different orderings to represent different messages. The total number of permutations can be calculated using the formula for permutations:

nPr = n! / (n - r)!

Here, n represents the total number of flags (6), and r represents the number of flags taken at a time (6). Therefore,

nPr = 6! / (6 - 6)! = 6! / 0! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Hence, using exactly six flags, the signal lac can send 720 messages.

b. Using exactly five flags:
In this case, we can select 5 flags out of 6 and arrange them in different orderings. The total number of permutations can be calculated using the formula for combinations:

nCr = n! / (r! × (n - r)!)

Here, n represents the total number of flags (6), and r represents the number of flags taken at a time (5). Therefore,

nCr = 6! / (5! × (6 - 5)!) = 6! / (5! × 1!) = 6

However, we need to consider that the blue flag must be included in all messages. Therefore, there is only one arrangement of the flags when using exactly five flags.

Hence, using exactly five flags, the signal lac can send only one message.