Final answer:
To find the number of distinct ways to rearrange the letters in 'racecar', we can use the concept of permutations. The number of distinct ways to arrange these 6 letters is 720. Option (C) is correct.
Step-by-step explanation:
A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}. As you can see, there are no other ways to arrange the elements of set A.
It is a mathematical calculation used for data sets that follow a particular order. Permutation differs from combinations; they are two different mathematical techniques. It is further classified into four types—repetitive, non-repetitive, circular, or multisets.
To find the number of distinct ways to rearrange the letters in 'racecar', we can use the concept of permutations. There are 7 letters in total, but the letter 'r' appears twice, so we can treat it as one letter. Therefore, we have 6 distinct letters to arrange.
The number of distinct ways to arrange these 6 letters is 6!
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.