One ordering of the letters T, U, V and Wfrom left to rightis UTVW. What is the total number of orderings of these letters from left to right, including UTVW?
4x3x2x1 = 24
24
To find the total number of orderings, we need to determine the number of permutations of the given letters.
We have four letters: T, U, V, and W.
The number of ways to arrange these letters can be calculated using the formula for permutations of n objects, which is n factorial (n!).
Therefore, the total number of orderings is:
4! = 4 x 3 x 2 x 1 = 24.
So, there are 24 orderings of the letters T, U, V, and W from left to right, including the ordering UTVW.
To find the total number of orderings of the letters T, U, V, and W from left to right, we can use the concept of permutations.
In this case, we have 4 letters to arrange. When one of the letters is fixed in a specific position (UTVW), we have 3 remaining letters to arrange in the other three positions.
Therefore, the number of orderings with UTVW fixed is 3! (read as 3 factorial). The factorial of a number is the product of all positive integers less than or equal to that number. In this case, 3! = 3 x 2 x 1 = 6.
So, there are 6 orderings of the remaining letters (T, V, and W) when UTVW is fixed.
Including the fixed order UTVW, the total number of orderings becomes 6 + 1 = 7.