Combinatorics

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?

How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?

Three cards were drawn from a pack of $$52$$ cards. The probability that they are a king, a queen, and a jack is

A box contains $$25$$ parts of which $$10$$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is

A box contains $$2$$ washers, $$3$$ nuts and $$4$$ bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing $$2$$ washers first f...