1. ## Probability.

Fifteen telephones have just been received at an authorized service center. Five are cellular, five are cordless, and five a conventional corded phones. If phones are randomly selected for service what is the probability that all the cordless phones are serviced first? What is the probability that after servicing ten phones, only two of the three types remain to be serviced?

My Work

Cellular - 5
Cordless - 5
Corded - 5

Sorry I don't know how to put the problem in Math symbol.

a) What is the probability that all the cordless phone are service first?
(5C5)(10C1)/(15C3) = (1)(10)/455 = .02 or 2%

b) What is the probability that after servicing ten telephones, only two of the three type remain to be service?
All I can come up is (10C2)(___)/(15C3)

2. Hello, iMoons!

Here's the first part . . .

Fifteen telephones has just received at a service center.
Five are cellular $\displaystyle (A)$, five are cordless $\displaystyle (B)$, and five conventional corded phones $\displaystyle (C)$.

(a) If phones are randomly selected for service, what is the probability
. . .that all the cordless phones $\displaystyle (B)$ are serviced first?
There are: .$\displaystyle {15\choose5,5,5} \,=\,756,\!756$ possible orders for the 15 phones.

There is one way for the $\displaystyle B$-phones to be first.

The other 10 phones can follow in: .$\displaystyle {10\choose5,5} \,=\,252$ ways.

Hence, there are: .$\displaystyle 1\cdot252 \:=\:252$ ways for the $\displaystyle B$-phones to be first.

Therefore: .$\displaystyle P(B\text{-phones first}) \;=\;\frac{252}{756,\!756} \;=\;\frac{1}{3003} \;\approx\;0.000333$

I'm still working on the second part . . .
.

3. I thought $\displaystyle 15C3 = 455$ or $\displaystyle {15\choose 3} \,=455$ because 15 way out of 3 types.