Question

The corners of standard tetrahedrons are unit numbers one, 2, 3, and 4. and 3 tetrahedrons are unit tossed. The likelihood that the total of upward corners is five is
A) \[\dfrac{5}{{24}}\]
B) \[\dfrac{5}{{64}}\]
C) \[\dfrac{3}{{32}}\]
D) \[\dfrac{3}{{16}}\]

Answer 1

Hint: First of all, we have to find the total number of possible cases that will come when the tetrahedra are tossed. And then find the total number of desired cases according to the question. and then we will divide the total number of desired cases by the total number of possible cases. Hence, we will get an answer.

Complete step by step solution: 
Now, according to the given question, we have three tetrahedrons that are tossed and there are a total of four faces on the tetrahedron. Therefore, the total number of possible cases will be,
\[ \Rightarrow 4 \times 4 \times 4\]
So, we will get it.
\[ \Rightarrow 64\]
According to the given question, the sum of the upward corners will be 5. So, the number of desired cases will be,
 \[ \Rightarrow \] (1, 2, 2), (2,2,1), (2,1,2), (1,1,3), (3,1,1), (1,3,1)
So, the total number of desired cases will be = 6
Therefore, The probability = \[\dfrac{6}{{64}}\]
\[ \Rightarrow \frac{3}{{32}}\]
So, the final answer will be \[\dfrac{3}{{32}}\].
Therefore, the correct option is (C).

Note: In this question, the first point is to keep in mind that the total number of possible cases in one tetrahedron is 4. And the probability is always determined with the help of the total number of cases.