Four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Count the number of elements in the event that no box contains a card with the same letter as the box.

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.

answer: a.   one is a factor of every whole number since every number is divisible by itself.