nCr=n!(n−r)!r!
nCr−1=n!(n−(r−1))!(r−1)!
nCr÷nCr−1=n!(n−r)!r!÷n!(n−(r−1))!(r−1)!
= n!(n−r)!r!×(n−(r−1)!(r−1)!n!
= (n+1−r)!(r−1)!(n−r)!r!
= (n+1−r)(n−r)!(r−1)!(n−r)!r(r−1)!
= n+1−rr