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Number of digits = 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Number of digits used = 4 For a 4-digit number, zero may not occupy box 1. Number of permutations for box 1 = Number of ways filling boxes 2, 3, 4 = Total number of 4-digit numbers = 9 x 1000 = 9000. - Wired Faculty

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Permutations And Combinations

Question

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Find the number of 4-digit numbers in which any digit may be repeated any number of times.

Solution

Number of digits = 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Number of digits used = 4

For a 4-digit number, zero may not occupy box 1.
Number of permutations for box 1 = $straight P presuperscript 9 subscript 1 space equals space fraction numerator 9 factorial over denominator 8 factorial end fraction space equals space 9$
Number of ways filling boxes 2, 3, 4 = $straight n to the power of straight r space equals space 10 cubed space equals space 1000.$
Total number of 4-digit numbers = 9 x 1000 = 9000.

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Permutations And Combinations

Find the number of 4-digit numbers in which any digit may be repeated any number of times.

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