Question

How many different ways can the letters in the word “survey” be arranged?

5040

1005

720

700

Answer 1

To determine the number of different ways to arrange the letters in the word "survey" which has six unique letters, we calculate the factorial 6!, resulting in 720 different permutations.

Step-by-step explanation:

The question asks for the number of different ways the letters in the word "survey" can be arranged. This is a problem of counting permutations because the order of the letters matters. The word survey consists of six unique letters. To find the number of permutations, we can use the factorial notation. The number of permutations of six unique items is represented by 6! (six-factorial), which is equal to 6×5×4×3×2×1.

Thus, the calculation would be:

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Therefore, there are 720 different ways to arrange the letters of the word "survey".

Answer 2

Square and survey each have 6 letters, none of which are repeats. For the first position there are 6 possibilities, then 5 (6 minus the one you already used), and so on, or 6 factorial (6!). 6x5x4x3x2x1 = 720, so there are 720 combinations for each. I hope this helps!