Combinatorics · Counting pairs · Complementary counting · Arrangements of digits · Binomial coefficients
(a) In how many ways can one choose two two-digit numbers that are not neighbours, that is, whose difference is not equal to \(1\)?
(b) How many five-digit numbers are there in which the digit \(5\) occurs exactly twice, while the remaining three digits are three distinct elements of the set \(\{1, 2, 3, 4, 6, 7\}\)?
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Serbian Regional Competition 2008, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source