IMO 1989 LL INA45

The expressions a + b + c, ab + ac + bc, and abc are called the

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IMO 1989 LL INA45

Origin: INA

Problem

The expressions a + b + c, ab + ac + bc, and abc are called the elementary symmetric expressions on the three letters a, b, c; symmetric because if we interchange any two letters, say a and c, the expressions remain algebraically the same. The common degree of its terms is called the order of the expression. Let Sk(n) denote the elementary expression on k different letters of order n; for example S4(3) = abc + abd + acd + bcd. There are four terms in S4(3). How many terms are there in S9891(1989)? (Assume that we have 9891 different letters.)