Question 19 of 28beginner🔧 ApplyNumerical2 marks

How many 5-digit passwords are possible?

Correct Answer

Given: Each digit has 10 choices (0-9).

Formula: Total combinations = 10×10×10×10×10=10510 \times 10 \times 10 \times 10 \times 10 = 10^5

Calculation:

105=100,00010^5 = 100,000

Answer: 100,000 (or 10510^5) passwords are possible.

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

Explanation

Each digit has 10 choices (0-9). For a 5-digit password, the total number of combinations is 10×10×10×10×10=105=100,00010 \times 10 \times 10 \times 10 \times 10 = 10^5 = 100,000. The chapter explains this with the progression: 2-digit lock has 102=10010^2 = 100 combinations, 3-digit lock has 103=100010^3 = 1000 combinations, so 5-digit lock has 105=100,00010^5 = 100,000 combinations.

Solution Steps

  1. Step 1: Each digit has 10 choices (0-9)

  2. Step 2: For 5 digits, total combinations = 10×10×10×10×10=10510 \times 10 \times 10 \times 10 \times 10 = 10^5

  3. Step 3: 105=100,00010^5 = 100,000

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