self Maths Puzzle

For an examination, a candidate has to select 7 subjects from three different groups X, Y and Z which contain 5, 6 and 4 subjects respectively. In how many different ways can a candidate make his selection if he has to select at least 2 subjects from each group?

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self Other Question

A new flag is to be designed with seven vertical strips using some or all of the colours Blue, Red, Black, White and Yellow. No two adjacent strips should be of the same colour. The number of ways this can be done such that even numbered strips are of the same colour while two consecutive odd numbered strips are of the same colour while two consecutive off numbered strips have different colours is A box contains 3 different White balls, 4 different Blue balls, 5 similar Green balls. In how many ways can 3 balls be drawn the box so that at least 1 blue ball is always included in the draw?