There are three boxes X, Y and Z each box contai nail paints of six different colours peach, wine, grey, olive, neon and violet respectively.

Pie chart given below shows the percent distribution of number of nail paints of five different colour peach, wine, grey, olive, and violet in box Z.

Probability of selecting two olive colour nail paint from box Y is (1/156) more than the probability of selecting two Violet colour nail paints from box X.

Total number of ways in which two Neon nail paints can be selected at random from box X is 105.

Total number of ways in which two Olive colour nail paints can be drawn at random from box Z is 15 and the probability of drawing a grey colour nail-paint from box Z is (1/5).

A.) If four nail paints are selected at random (two from box X and two from box Z), then what is the probability that one nail paint from box Z is Wine and other is Grey and one nail-paint from box X is Violet and other is Peach?

B.) If in the box Y, some number of Black nail paints are also added, then the probability of selecting one Neon nail paint becomes 1/3. Now, 5 nail paints are selected at random from box Y, then in how many numbers of ways this can be done in which at least 3 nail paints are black color?

C.) What is the ratio of total number of ways in which out of total 5 drawn nail paints from box Z, 2 are Violet, 3 are Grey to the total number of ways in which out of total 4 drawn nail paints from box X, 1 is Violet, 1 is Wine and 2 are Peach?

10% 20% 15% 30% 25% IPeach Wine Grey Olive Violet Line graph given below shows the number of peach, wine, grey, olive, and violet colour nail paints in boxes X and Y together respectively. 12 10 4 Peach Wine Grey Olive Violet 2.