6n3 − 96n2 + 176n − 96Р 2, 1, 1, 1 4 4 =Р 3 3 24Р n − 1 n − 1 n4 − 10n3 + 35n2 − 50n + 24Р 1, 1, 1, 1, 1 1 =Р 4 4 24Р (Note that in the second and third cases we need n ≥ 2, in the fourth and fifth cases weР need n ≥ 3, in the sixth case we need n ≥ 4, and the seventh case we need n ≥ 5. In eachР case, though, the given formula works for smaller positive values of n since it is equal toР 0 in each case. Note also that we say b = 1 in the first case since there is exactly 1 way ofР placing 0s in all of the remaining n − 1 positions.)Р f(n) is then the sum of the expressions in the last column of this table, and soР n4 + 6n3 + 11n2 + 6n n(n + 1)(n + 2)(n + 3)Р f(n) = =Р 24 24Р as required.Р Method 2Р First, we create a correspondence between each integer with n digits and whose digits have
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