q: Ten telegenic contestants with a variety of personality disorders are to be divided into two "tribes" of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
Options:
(A) 120
(B) 126
(C) 252
(D) 1200
(E) 1260
a: OK... My ans is 10C3 = 120
The answer is (A).

q: A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?
Options:
(A) 6
(B) 8
(C) 10
(D) 12
(E) 15
a: OK... If students are A, B, C, D, E and F; we can have 6C3 groups in all. However, if we have to count groups in which a particular student (say A) is always selected we would get 5C2 = 10 ways of doing it.
The answer is (C).

q: One red flower, three white flowers and two blue flowers are arranged in a line such that
I. No two adjacent flowers are of the same colour.
II. The flowers at the two ends of the line are of different colours.
In how many different ways can the flowers be arranged?
Options:
(A) 6
(B) 4
(C) 10
(D) 12
(E) 14
a:
OK... The total possibilities are W@W@W@ (or) @W@W@W, where 2 blue and 1 red flowers occupy the space marked as @. Hence, the Total number of permutations is 2 x (3! / 2!) = 6.
The answer is (A).