Question

1. engel has to make a 5-digit passcode from six different digits—1, 2, 3, 4, 5, and 6. no digit can be used more than once in a passcode. how many different passcodes can engel create?

Explanation:

Step1: Determine permutation type

Permutation of 6 digits taken 5 at a time (no repetition).

Step2: Apply permutation formula

Formula: $P(n,k)=\frac{n!}{(n-k)!}$, where $n=6$, $k=5$.

Step3: Calculate the value

$P(6,5)=\frac{6!}{(6-5)!}=\frac{6×5×4×3×2×1}{1}=720$.

Answer:

720