Probably Probability

Probability, I love it. I really do, just that I'm not that good at it, and due to that, I don't really fancy it. Now, trigo,more like my thing.
But, just to show you how complicated things can be with probability, I'm gonna give u a question I haven't been able to solve. Like Pn Erwani said " Cerita dia panjang, tapi solution dia dua baris je. Boringnya.! Kena faham cerita dia dulu. " haha.

Here's the question. Warning, reading this means you are hereby required to answer this question, I don't care, give me rubbish answers, I just want an answer! Compulsory okay, if not, click the red box with a white cross on the top right hand corner of the screen. :P
There are 350 students in an academy for pre-degree programme. They are divided into a certain number of classes (not important). As they progress into degree progamme, only 100 students will be chosen from the previous 350. As they progress into the masters programme, only 50 of the previous 100 will be chosen, and in the PhD programme, only 25 of the previous 50 students will be chosen to do it.
Now, in a certain pre-degree programme class, there are 16 students. The teacher, Pn Erwani expects 7 of them to progress into degree level, and those same 7 to progress into masters level and the very exact same 7 from the beginning to progress to Ph.D level.! Simply find the probability that these 7 students from that class will be chosen from the pre-degree level all the way into Phd level.

Lets name these 7 students for better comprehension,
Niko
Ker
Sawi
Irsyad
Dahiyah
Jessica
Tingtong

Niko, Ker, Sawi , Irsyad, Dahiyah, Jessica and Tingtong are from class Alpha in the pre-degree programme. Same class okay. All of them progress into degree, masters and finally PhD.

Find the probability that Niko, Ker, Sawi, Irsyad, Dahiyah,Jessica and Tingtong will progress all the way from pre-degree to PhD. :O

It's an amazingly low probability, like 7 of these guys will be part of the 25 finally chosen for Phd from the initial 350 of pre-degree. Wow. Try to figure it out please.

If you have, then. Look at this next statement to double check your answer.

Pn Erwani lowers her expectations after seeing the mid-year results, :D
She believes that Niko, Ker, Sawi, Irsyad, Dahiyah, Jessica and Tingtong will progress to degree level (still 7 people), but thinks that only Ker, Dahiyah, and Irsyad (3 only) will make it to masters level. Finally she completely lowers her expectations and thinks that Irsyad, just him will be able to make it to Ph.D level. Now find the probability that of the 16 students in her pre-degree class, only Irsyad makes it to PhD level!

The answer for the 2nd statement should be higher than the first right? Figure it out. Please.