# Question :

There are 10 boxes with a combined weight of 75 kg. Their individual weights (in kilograms) are 15, 13, 11, 9, 8, 4, 2, 2 and 1.

You have to pack the boxes into three crates but each crate can hold a maximum of 25 kg. The boxes with weights 9 kg, 10 kg and 11 kg must be in different boxes. The boxes with weight 2kgs cannot be paired with the 13 kg weight box.

What arrangement should be used?

# Solution :

Boxes in boxes!! Let us try and solve this.

There is only one arrangement available. One of the bigger boxes will include the 15 kg box and the 10 kg box. The second bigger box will include 13 kg, 11 kg and 1

kg box. The final bigger box will hold the 9 kg, 8 kg, 4 kg and the two 2 kg boxes.

Place a single red ball in one jar, say jar 1, and all the remaining balls in the other jar, say jar 2.

• For jar 1, you will have a 1/2 chance of picking jar 1, and then 1/1 chances of it being the red ball.
• For jar 2, you will again half 1/2 probability of selecting the jar 2, and then 49/99 chances of picking up a red ball.

Total chances are : 1/2 + (1/2)(49/99)

which gives 74/99, almost 3/4 chances of picking a red ball.

# Thanks for Reading

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