How many four-digit numbers can be formed using the digits 1,2,3,4,5,6,7 if adjacent digits must be different

Please explain how I might arrive at the answer. Thank you!

The answer is 7·6³.

Explanation: the first digit may be chosen at random among all 7. When choosing each of the next three digits we only have 6 to choose from since one is always ruled out being a repetition of the preceeding digit.

You have 7 choices for the first, 6 for the second, 6 for the third, and 6 for the 4th. so its 7x6^3 = 7x216 = 1512

If you start with 1, the next must be 2 through 7 (6 choices). If you choose 7, for example, the next must be 1 through 6 (6 choices), etc.

Permutation of 4 from 7
7!/(7 - 4)! = 5*6*7 = 210

23

if to be arranged or not it should be 7C4