Give geometric representation for followings:

i) { -3} x R
ii) {1, -2) x ( 2, -3) 

How many ways are there to distribute 10 district objects into 4 distinct boxes with:

i) At least two empty box.
ii) No empty box.

How many words can be formed using letter of DEPARTMENT using each letter at most once?
 i) If each letter must be used,
 ii) If some or all the letters may be omitted.

There are two mutually exclusive events A and B with P(A) =0.5 and P(B) = 0.4. Find the probability of followings:
i) A and B both occur
ii) Both A and B does not occur 

How many different committees can be formed of 10 professionals, each containing at least 2 Project Managers, at least 3 Team Leaders and 1 Vice President.