In this case we need to find how many possibilities if 5 flags are used, then 4 flags, then 3 flags, then 2 flags and then 1 flag and add up the possibilities.

If 5 flags are used then the number of possibilities is 5*4*3*2* 1 or 120 possibilities.

If 4 flags are used then the number of possibilities is 5*4*3*2 or 120 possibilities.

If 3 flags are used then the number of possibilities is 5*4*3 or 60 possibilities.

If 2 flags are used then the number of possibilities is 5*4 or 20 possibilities.

If 1 flag is used then the number of possibilities is 5.

Then add up the possibilities 120 + 120 + 60 + 20 + 5 = 325 or choice B.

Take care,
Sionainn

vaibhav101 wrote:How many signals can be made with 5 different flags by raising them any number at a time?

A 375
B 325
C 475
D 275
E 625

If we only raise 1 flag at a time, there are 5P1 ways to raise it.

If we raise 2 flags at a time, there are 5P2 ways, to raise them.

Using the same logic, there are 5P3, 5P4 and 5P5, ways to raise 3, 4, and 5 flags at a time, respectively. Therefore, the total number of ways to raise any number of flags at a time is:

5P1 + 5P2 + 5P3 + 5P4 + 5P5 = 5 + 20 + 60 + 120 + 120 = 325

Answer: B