Respuesta :
Answer:
Step-by-step explanation:
To assign 4 different tasks to 4 students, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.
Since each task is different and each student is assigned only one task, we can use the permutation formula to calculate the number of ways to assign the tasks:
\[ \text{Number of ways} = n! \]
Where \( n \) is the number of tasks (4 in this case) and \( ! \) denotes factorial.
So, for 4 tasks, the number of ways to assign them to 4 students is:
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]
Therefore, there are 24 possible ways for the teacher to assign 4 different tasks to her 4 students.
To calculate the number of ways to draw the first, second, and third prizes from a box containing 120 names, we can use the concept of permutations.
For the first prize, there are 120 names to choose from. Once the first name is drawn, there are 119 remaining names for the second prize, and once the first two names are drawn, there are 118 remaining names for the third prize.
Therefore, the number of ways to draw the first, second, and third prizes is given by the permutation formula:
\[ \text{Number of ways} = 120 \times 119 \times 118 \]
\[ = \frac{120!}{(120 - 3)!} \]
\[ = \frac{120 \times 119 \times 118}{3 \times 2 \times 1} \]
\[ = 120 \times 119 \times 118 \]
\[ = 168,168,0 \]
So, there are 168,168,0 possible ways to draw the first, second, and third prizes from a box containing 120 names.
