(in c++, without using #include <iostream.h>, <stdio.h>, <assert.h> or <conio.h>

Question

(in c++, without using #include <iostream.h>, <stdio.h>, <assert.h> or <conio.h>)

The formula for computing the number of ways of choosing r different things from a set of n things is the following:

C(n, r) = n! / (r! * (n – r)!)

The factorial function n! is defined by

n! = n * (n – 1) * (n – 2) * ... ·*1

Discover a recursive version of this formula and write a recursive function that computes the value of the formula. Using this recursive function, write a function which computes the formula for number of ways to choose r different things from a set of n things.

Then write a program that takes r and n as user input, then calls the above functions and outputs the result.

Hint: some of the intermediate values (such as 16!) are too large to fit in a variable of int type. Consider using a type which can store larger numbers such as long (or even unsigned long, since our numbers are all positive in this problem).

The program should print a string of text to the terminal before getting each line of input from the user. A session should look like the following example (including whitespace and formatting), with possibly different numbers in the output:

Explanation / Answer

Output:

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