function wys = ways(members committee) where members is the total number of club

function wys = ways(members committee)
where members is the total number of club members and committee is the size of the committee. The function must be based on the following logic:
To calculate ways(m c) suppose Ann is a member of the club. A committee either includes Ann or does not include Ann
If the committee includes Ann it also must have c-1 other members and these must be chosen from the m-1 club members besides Ann. So the number of ways to make a committee with c members including Ann is the same as the number of ways to choose a committee of c-1 from m-1 members i.e. ways(m-1 c-1)
If the committee does not include Ann it has to have c members from the m-1 club members other than Ann so there are ways(m-1 c) ways to choose such a committee.
So in total there are ways(m-1 c-1) + ways(m-1 c) different committees of c people chosen from m club members.
Note that there are m ways to choose a committee of 1 person out of m members and only one way to choose a committee of m people out of m members