Telephone calls

MURALIDHARGAJULA wrote:A company has 8 telephone lines. IF 4 calls have to be made by the company , what is the probability that they are each made on a different line?

Total number of ways to make 4 calls using 8 lines = 8^4

But we have to make calls on different lines.
Hence, we have to select 4 lines out of 8 and distribute the 4 calls in those selected lines. Which can be done in (8C4)*4! ways

Therefore, required probability = (8C4)*4!/(8^4) = 8*7*5*6/8*8*8*8 = 105/256

The correct answer is B.

ganesh prasath wrote:"Hence, we have to select 4 lines out of 8 and distribute the 4 calls in those selected lines. Which can be done in (8C4)*4! ways"

I didnt understand this part could u please explain this to me..

The company has 8 lines and they have to make 4 calls each on different line. Hence they need 4 different lines to do so. Hence, we are selecting 4 lines out of 8 lines in 8C4 ways.

Now we have to assign the 4 calls to these 4 selected lines. Which can be done in 4! ways, because the first call can be made in any of the 4 selected lines. The second call can be made in any of the remaining 3 selected lines. The third call can be made in any of the remaining 2 selected lines. And the fourth and last call can be made in the remaining selected line.

Hence, we can assign the 4 calls to these 4 selected lines in 4*3*2*1 = 4! ways

Hope it helps.