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Chapter 5: Problem 444

The number of 4 digits number which do not contain 4 different digit is (a) 2432 (b) 3616 (c) 4210 (d) 4464

Short Answer

Expert verified
The number of 4-digit numbers which do not contain 4 different digits is 4464.

Step by step solution

01

Calculate Total 4-Digit Numbers

Calculate the total number of 4-digit numbers. Since the first digit can be any of the 9 numbers 1 to 9 and the remaining 3 digits can be any of the 10 numbers 0 to 9, there are 9 × 10 × 10 × 10 = 9000 possible 4-digit numbers.
02

Calculate 4-Digit Numbers with 4 Different Digits

For a 4-digit number with all 4 digits different, the first digit can be any of the 9 numbers 1 to 9. For the second digit, there are 9 remaining options (0 to 9, excluding the first digit). The third digit can be any of the 8 remaining options, and the fourth digit can be any of the 7 remaining options. So, there are 9 × 9 × 8 × 7 = 4536 4-digit numbers with 4 different digits.
03

Calculate 4-Digit Numbers with at Least One Repeated Digit

Since we have already calculated the total number of 4-digit numbers and the number of 4-digit numbers with 4 different digits, we can now find the number of 4-digit numbers with at least one repeated digit by subtracting these two values: 9000 - 4536 = 4464. So, there are 4464 4-digit numbers with at least one repeated digit.
04

Choose the Correct Answer

Comparing this result with the given answer choices, we find that the correct answer is (d) 4464.

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Most popular questions from this chapter

\(\mathrm{ABCD}\) is a convex quadrilateral. \(3,4,5\) and 6 points are marked on the sides \(\mathrm{AB}, \mathrm{BC}, \mathrm{CD}\) and \(\mathrm{DA}\) resp. The number of triangles with vertices on different sides are (a) 270 (b) 220 (c) 282 (d) 342

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