4 students are sitting to receive the prizes.Alan and Julia wanted to sit together, how many different arrangements of students would there be ?
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sorry,i am still not understand
To find the number of different arrangements of the students, we first need to determine the number of ways Alan and Julia can be seated together. We can treat Alan and Julia as a single entity or block. Then, we have 3 entities (block of Alan and Julia, and the other 2 students) to be arranged.
To calculate the number of arrangements of these 3 entities, we use the concept of permutations. This is because the order in which the entities are arranged matters.
The number of permutations of n objects taken r at a time is given by nPr = n! / (n-r)!. Here, n is the total number of objects, and r is the number of objects taken at a time.
In this case, we have 3 entities to be arranged, so n = 3.
Now, we calculate the permutations when 3 objects are taken at a time:
3P3 = 3! / (3-3)! = 3! / 0! = 3! / 1 = 3
So, there are 3 different arrangements of the 3 entities.
Now, within each of these arrangements, Alan and Julia can be seated together or vice versa. In each of the 3 arrangements, Alan and Julia can be seated next to each other in 2 different ways: Alan on the left or Alan on the right.
Therefore, the total number of different arrangements with Alan and Julia sitting together is 3 x 2 = 6.
Hence, there would be 6 different arrangements of the students if Alan and Julia were to sit together.