Gate Exam

In how many ways can a given positive integer n 3 be expressed as the sum of 3 positive
integers (which are not necessarily distinct). For example, for n = 4, the number of ways is 3,i.e., 1+2+1, 2+1+1. Give only the answer without any explanation.

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Gate Other Question

In how many ways can a given positive integer n 2 be expressed as the sum of 2 positive integers (which are not necessarily distinct). For example, for n = 3, the number of ways is 2, i.e., 1+2, 2+1. Give ANSWER?? What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?
(113.+111.)+ 7.51
113.+(111.+ 7.51)
(a) 9.51 and 10.0 respectively
(b) 10.0 and 9.51 respectively
(c) 9.51 and 9.51 respectively
(d) 10.0 and 10.0 respectively.