Question

Two cubical dice each have removable numbers 1 through 6. The twelve numbers on the two dice are removed, put into a bag, then drawn one at a time and randomly reattached to the faces of the cubes, one number to each face. The dice are then rolled and the numbers on the two top faces are added. What is the probability that the sum is 7

1. Jezebel
The probability that the sum is 7 of the numbers that appears on the both cubical dice is 2/11.

### What is combination?

A combination would be a method of picking elements out of a collection in which the orientation of selection is irrelevant. Assume we have three numbers P, Q, and R.
Combination defines how many possibilities we may choose two digits from each set.
Now, according to the question;
We presume that the numerals are different colors. There are two dice, each with a value ranging from 1 to 6. After the toss, the probability of receiving any two colors is the same.
For combination of 2 colours out of 12 is given by;
¹²C₂ = 12!/{2!(12-2)!}
¹²C₂ = 66 such combinations are possible.
The given condition is, the sum of 7 should appear on the faces of dice.
The possible combinations are-
(1+6), (2+5), (3+4) such 3 pair of numbers are possible.
Because each number inside the bag contains two different colors, each of these three alternatives corresponds to four different color combinations.
Occurrence of 7 comes with 3×4 = 12 pairs.
Thus, the requires probability is;
Probability = 12/66
= 2/11
Therefore,  the probability that the sum is 7 on the both faces of cubical dice is 2/11.
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