Respuesta :
Answer:
There are total of 23 events in which the box DO NOT get the SAME label card as the box.
Step-by-step explanation:
Here, the total number of boxes = 4
A , B , C and D
There are a total of 4 cards with same label A, B , C and D.
Now, the total number of ways, by which the 4 cards can be placed in 4 boxes RANDOMLY as
= 4 x 3 x 2 x 1 = 24 ways
Now, the number of ways, the each box with same number has the EXACT SAME card
= 1 way which is A in A , B in B , C in C and D in D
So, the number of ways where no box contains a card with the same letter as the box
= Total ways - The ways with same number has the EXACT SAME card
= 24 ways - 1 way = 23 ways
Hence, there are total of 23 events in which the box DO NOT get the SAME label card as the box.
There number of elements in the events that no box contains card with the same letter as the box can be arranged in 24 ways.
What is Permutation?
A permutation is a mathematical computation that determines the number of different ways a given set may be organized, with the order of the arrangements being taken into consideration.
From the given information:
The four cards that are randomly placed in the four boxes can be represented by using the permutation method and can be expressed as:
[tex]\mathbf{ = ^4P_4}[/tex]
Since no box contains a card with same letter as the box, It implies that:
- Card A can be placed in a box in 4 ways,
- Card B can be placed in a box in 3 ways,
- Card C can be placed in a box in 2 ways,
- Card D can be placed in a box in 1 way.
Thus, the Permutation of the four cards can be calculated as:
[tex]\mathbf{^4P_4 = \dfrac{4!}{0!}}\\ \\ \mathbf{= \dfrac{4 \times 3 \times 2 \times 1}{0}} \\ \\ = 24 \ ways[/tex]
Learn more about Permutation here:
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