How many distinct 4-digit codes can be formed using the digits 0 through 9 if repetition of digits is strictly prohibited and the first digit cannot be 0?
Answer and explanation
Correct answer: D. 4,536
- Step 1: Apply the Fundamental Counting Principle across the 4 position slots:
- Step 2: Slot 1 (thousands place): Cannot be 0, so choices are {1, 2, ..., 9} = 9 options.
- Step 3: Slot 2 (hundreds place): Any digit from 0 to 9 except the one chosen for slot 1 = 9 options (since 0 is now allowed).
- Step 4: Slot 3 (tens place): Any remaining digit from the 8 unselected digits = 8 options.
- Step 5: Slot 4 (units place): Any remaining digit from the 7 unselected digits = 7 options.
- Step 6: Total codes = 9 9 8 * 7 = 4,536.
Answer
4,536.
Why not the others: '5,040' is 10 9 8 7 (allowing 0 as first digit); '3,024' is 9 8 7 6 (forgetting that 0 becomes available after slot 1); '9,000' is 9 10 10 * 10 (with repetition allowed).
Practise more Geometry, Trigonometry, and Quantitative Problem Solving.
Free questions with an explanation for every one, and full timed Kuwait University Aptitude Tests (KUAT) mock tests.
More Geometry, Trigonometry, and Quantitative Problem Solving questions
- What is the exact value of sin(75 degrees)?
- Find all solutions for theta in the interval [0, 2pi) that satisfy: 2 cos^2(theta) - cos(theta) - 1 = 0.
- In triangle ABC, side a = 7 cm, side b = 5 cm, and the included angle C = 60 degrees. Find the exact length of side c using the Law of Cosin…
- Find the center and radius of the circle defined by the equation: x^2 + y^2 - 6x + 8y - 11 = 0.
- What is the equation of the line passing through point (4, -2) that is perpendicular to the line 3x + 2y = 8?
- A right circular cylinder has a height of 12 cm and a total surface area of 110pi cm^2. What is the radius of its base?