Suppose n and p are unsigned int variables in a C program.

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Suppose n and p are unsigned int variables in a C program. We wish to set p to ⁿC₃ . If n is large, which one of the following statements is most likely to set p correctly?

1. p = n*(n – 1)*(n – 2)/ 6;
2. p = n*(n – 1)/ 2*(n – 2)/ 3;
3. p = n*(n – 1)/ 3*(n – 2)/ 2;
4. p = n * (n - 1) * (n – 2)/ 6.0;

Correct Option: B

P = ⁿC₃

=	n(n - 1)(n - 2)
	6

If we multiply, n, (n – 1) and (n – 2) together, it may go beyond the range of unsigned integer. (\ option (a) and (d) are wrong) For all values of n, n(n – 1)/2 will always be an integer value, But for n(n – 1)/3, it is not certain.
Take options (b)

P =	n(n - 1) / 2	×	(n - 2) / 3
	P₁		P₂

P₁ will be having no error, thus P will be more accurate Option (c)

P =	n(n - 1) / 3	×	(n - 2) / 2
	P₁		P₂

There is possibility of truncation in P₁, the accuracy of P is less