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.

a. how many combinations of five digits from the digits 1, 2, 3, 4, 5, and 6 are possible?

Explanation:

Step1: Identify the problem type

This is a combination problem where we need to choose 5 digits from 6 distinct digits. The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 6 \) (total digits) and \( k = 5 \) (digits to choose).

Step2: Substitute values into the formula

Substitute \( n = 6 \) and \( k = 5 \) into \( C(n,k) \):

$$
LATEXBLOCK0
$$

Answer:

6