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In the (a) part, the number of 3 digit numbers that can be formed from the digits is given by 9 x 10 x 10 = 900 (3 digit numbers). It should be noted that no number begins with zero.
In the (b) part, the smallest number divisible by 3 is 102 while the biggest number is 999. Thus from the A.P, 999 = 102 + 3(n – 1) where n = 300.
Similarly, the smallest number divisible by 9 is 108 while the biggest number is 999. this implies that 999 – 108 + 9 (n – 1) which gives n = 100.
In the (c) part, the required sum is the sum of numbers divisible by 3 minus the sum of numbers divisible by 9 which is given by
300 (102 + 999) - 100 (108 + 999) = 109800 .
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