probability 1

This is a very elementary solution. We clearly see that the Boss Lan has $30$ choices for the person to be sent to Singapore. Then, he has $29$ choices for the person to be sent to England, as already $1$ person was alloted for Singapore. With similar reasoning, we find that the number of choices for America, Japan and India (My Motherland !) are $28, 27$ and $26$ respectively. As all these allotments are independent of their order [i.e., the boss can first choose for England, then India, and so on and the order does not matter] and are independent events, we can use the rule of product to see that the number of ways the people can be allotted are $30 \times 29 \times 28 \times 27 \times 26 = 17100720$ .

There's $_{30}C_{5}$ ways to choose the employees who are going, and there's $5!$ ways to send each of them off to a different country. So you have...

$\frac{30!}{25! \ 5!} * 5! = \frac{30!}{25!} = 30*29*28*27*26 = \boxed{17100720}$ ...choices of possible arrangements. It's not the fastest way to get to the answer, but it made the most sense to me.

I found the wording of the question a little ambiguous though. It took me all 3 tries to understand exactly what he was asking, but that's just me. Did anyone else have a problem with it? I think the question should be stated differently.

The number of choice = (30C1)(29C1) (28C1) (27C1) (26C1)= 17100720

Well done Chris. Keep up the good work!