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How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits being allowed?
- a)12
- b)108
- c)256
- d)192
Correct answer is option 'D'. Can you explain this answer?
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How many numbers of four digits can be formed with the digits 0, 1, 2,...
To find the number of four-digit numbers that can be formed using the digits 0, 1, 2, and 3 with repetition allowed, we can break down the problem into four separate choices for each digit.
Choice for the first digit: Since the number cannot start with 0, we have three choices for the first digit (1, 2, or 3).
Choice for the second digit: We have four choices for the second digit (0, 1, 2, or 3).
Choice for the third digit: Again, we have four choices for the third digit (0, 1, 2, or 3).
Choice for the fourth digit: Lastly, we have four choices for the fourth digit (0, 1, 2, or 3).
Therefore, using the fundamental counting principle, the total number of four-digit numbers that can be formed is:
3 choices for the first digit × 4 choices for the second digit × 4 choices for the third digit × 4 choices for the fourth digit = 3 × 4 × 4 × 4 = 192.
Thus, the correct answer is option D: 192.
Choice for the first digit: Since the number cannot start with 0, we have three choices for the first digit (1, 2, or 3).
Choice for the second digit: We have four choices for the second digit (0, 1, 2, or 3).
Choice for the third digit: Again, we have four choices for the third digit (0, 1, 2, or 3).
Choice for the fourth digit: Lastly, we have four choices for the fourth digit (0, 1, 2, or 3).
Therefore, using the fundamental counting principle, the total number of four-digit numbers that can be formed is:
3 choices for the first digit × 4 choices for the second digit × 4 choices for the third digit × 4 choices for the fourth digit = 3 × 4 × 4 × 4 = 192.
Thus, the correct answer is option D: 192.
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How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits being allowed?a)12b)108c)256d)192Correct answer is option 'D'. Can you explain this answer?
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