A contestant has to arrange the events that correspond to A, B, C and D. One contestant is positive that event D follows directly after event B, but doesn't not know about the others. How many diffrent ways could this e the letters A,B,C and D.? list the possibilitiess.
If we assume that event D must directly follow event B, we have the following possibilities:
1. B -> D -> A -> C
2. B -> D -> C -> A
3. A -> B -> D -> C
4. C -> A -> B -> D
Therefore, there are four different ways the letters A, B, C, and D could be arranged based on the given condition.
To determine the different possible arrangements for the events A, B, C, and D given the information that event D follows directly after event B, we can consider the following steps:
1. Identify the fixed positions: We know that event D must follow event B. So, we can fix the positions of B and D as BD.
2. Arrange the remaining events: Now, we need to arrange the remaining events A and C around the fixed positions BD. Since there are two remaining events, there are two possible arrangements for them, AC and CA.
3. Combine the arrangements: Finally, we combine the fixed positions with the arrangements of the remaining events. So, the possible arrangements are:
- BDAC: Event B followed by D, followed by A, and then C.
- BDCA: Event B followed by D, followed by C, and then A.
Therefore, there are two different possible arrangements: BDAC and BDCA.