A student committee consists of 2 persons.These 2 people will be chosen from a group consisting of 6 senior level students, 7 intermediate level students and 4 junior level students . How many choices are possible if

(a) both people are chosen from the same level ;
(b) these 2 people are chosen from different levels .





I will be glad if someone help !

(a)

This could be:
1. 2 people from senior, that is 6C2
2. 2 people from intermediate, that is 7C2
3. 2 people from junior, that is 4C2

So, add them all!

(b)

_ _
These are the two slots. In the first slot, you can put any of the 17 people, so, you put:

(17) _

Now, if you picked from senior, you are left with 11 more people, so you put (17) (11). The number of choices becomes 17*11 = 187.

If you picked from intermediate, you are left with 10 more people, so you put (17) (10). The number of choices becomes 17*10 = 170.

Same for if you picked junior.

Add the three different configurations and you will get the answer.

I hope it helped! :) Post what you get!