Question

Twelve members of parliament are available for selction on a five person committe of enquiry. Seven of those available are from the opposition while five are from the government. Howe many such commitees are possible if each committee must contain more than two members from the opposition?

Answer 1

Or .... and getting the right answer:
We cannot have cases with no opposition and only one in opposition.
(7 in opposition, 5 in government)

number without any restriction = C(12,5) = 792
number with no opposition = C(7,0)*C(5,5) = 1
number with one from opposition = C(7,1)*C(5,4) = 35

Number as requested = 792-1-35 = 756

Answer 2

But your first answer was 2296, which was totally wrong

btw, where did you get 2100 from in your first answer ??

Answer 3

NOOO, that's where your mistake its

You said "the correct answer is C(7,3) * C(5,2) = 210 * 10 = 2100, not 840 as I had written.)

but the correct answer to C(7,3) * C(5,2) = 350 , not 2100 and not 840 !!!