The expression C(n,r) denotes the number of r -element subsets of an n -element

Question

The expression C(n,r) denotes the number ofr-element subsets of an n-element set. Thisis a combinatorial function pronounced as “n chooser”. For example, given a set of 4 colors
{ red, blue, green, yellow }, how many distinct sets of 2 colorscan we make? (Note: the sets { red, blue } and { blue,red } are not-distinct.) C(4,2)=6 , hencethere are six distinct subsets of 2 elements – { red, blue },{ red, green }, { red, yellow }, { blue, green }, { blue, yellow },and { green, yellow }. The value of C(n,r) is given bythe formula

Write a program in C that computes C(n,r) using the followingcomponent functions

i.       main(): prompts the user for two numbersstoring them in variables n andr respectively; and then prints theresult after C(n,r) is computed.

ii.      check(): compares r and n. If r >n or if r orn are negative, check()invokes the function err_msg() which prints anerror message. The program will then terminate.

iii.    comb(): computesC(n,r) .

iv.    fact(): computes afactorial.

Explanation / Answer

please rate - thanks #include #include bool check(int,int); void err_msg(); int comb(int, int); double fact(int); int main() {int c,r,n; bool valid; printf("How many elements in the set? "); scanf("%d",&n); printf("How large is the subset? "); scanf("%d",&r); if(check(n,r))    {c=comb(n,r);    printf("There are %dC%d = %d ",n,r,c);    } getch(); return 0; }                           bool check(int n, int r)    {if(r>n||r

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