A printer is printing out 3digit numbers between 100999 such

A printer is printing out 3-digit numbers between 100-999 such that the digits are not repeated. (a) If 2000 such numbers are printed out, at least how many if them will be identical? Justify your answer. (b) At least how many of the numbers should be printed, so that at least 3 of them will be identical? Justify your answer. (c) At least how many of the numbers should be printed, so that the number 243 is printed at least 6 times? Justify your answer.

Solution

(a)

No of ways printing the number (digits are not repeated) = 9*9*8 = 648

If 2000 such numbers are printed out, them will be identica1 = 2000-648 = 1352

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(b)

at least 3 of them will be identical

648 + (2 extras for indetical) = 650

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(c)

648+ (6-1) = 648+5 = 653