How many ways can the sequence ANNV be arranged
To find the number of ways the sequence ANNV can be arranged, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order, and its formula is given by:
P(n, r) = n! / (n - r)!
where n is the total number of objects and r is the number of objects being arranged.
In this case, we have the sequence ANNV. The sequence has 4 objects, but since we have duplicate letters (N), we need to take that into account.
Let's break it down step by step:
Step 1: Count the total number of objects.
In this case, we have 4 objects: A, N, N, V.
Step 2: Count the number of duplicate objects.
Here, we have 2 duplicate letters (N).
Step 3: Adjust the total number of objects.
Since we have duplicate letters, we need to divide the total number of objects by the factorial of the number of duplicate letters.
In this case, we divide 4! by 2! (factorial of 2, representing the number of duplicate N's).
Step 4: Use the permutation formula.
Plug in the adjusted values into the permutation formula:
P(n, r) = 4! / 2!
Calculating this gives us:
P(4, 2) = 4! / 2! = 4 * 3 * 2 * 1 / (2 * 1) = 24 / 2 = 12.
Therefore, there are 12 different ways the sequence ANNV can be arranged.