Question 20 of 28intermediate🔧 ApplyNumerical2 marks

Estu says, 'Next time, I will buy a lock that has 6 slots with the letters A to Z. I feel it is safer.' How many passwords are possible with such a lock?

Correct Answer

Given: A lock has 6 slots, each with 26 possible letters (A-Z).

Formula: Total combinations = 26×26×26×26×26×26=26626 \times 26 \times 26 \times 26 \times 26 \times 26 = 26^6

Calculation:

266=308,915,77626^6 = 308,915,776

Answer: 308,915,776 passwords are possible.

Exercise: How Many Combinations | Q: 1 | (Page Page 9)
For More Understanding

Explanation

Each slot can have any of the 26 letters (A-Z). For 6 slots, the total number of combinations is 26×26×26×26×26×26=266=308,915,77626 \times 26 \times 26 \times 26 \times 26 \times 26 = 26^6 = 308,915,776. This is much larger than a 5-digit numeric password (100,000), making it more secure.

Solution Steps

  1. Step 1: Each slot has 26 choices (A-Z)

  2. Step 2: For 6 slots, total combinations = 26626^6

  3. Step 3: 266=308,915,77626^6 = 308,915,776

PreviousNext