Question

1. biking talula got a new bicycle lock that has a four - number combination. each number in the combination is from 0 to 9.

a. how many combinations are possible if there are no restrictions on the number of times talula can use each number?
b. how many combinations are possible if talula can use each number only once? explain.

Explanation:

Part (a)

Step 1: Identify choices per digit

Each of the 4 digits in the combination has 10 choices (0 - 9).

Step 2: Apply multiplication principle

For 4 independent digits, total combinations = \(10\times10\times10\times10\)
\(10^4 = 10000\)

Step 1: First digit choices

First digit: 10 choices (0 - 9).

Step 2: Second digit choices

Second digit: 9 remaining choices (can't repeat first).

Step 3: Third digit choices

Third digit: 8 remaining choices (can't repeat first two).

Step 4: Fourth digit choices

Fourth digit: 7 remaining choices (can't repeat first three).

Step 5: Calculate total combinations

Total = \(10\times9\times8\times7\)
\(10\times9 = 90\), \(90\times8 = 720\), \(720\times7 = 5040\)

Answer:

10000

Part (b)