Why multiplication is used

#1

in recurrence relation
f(n)=1.f(n-1) + (n-1)c1.f(n-2) is used

why here multiplication is used ?

#2

hi @atkr030

each person has 2 options, either they can go alone, or they can take someone with them.
if they take a partner, they can choose a partner from N-1 remaining people in (n-1)C1 ways and the remaining answer can be found by f(n-2). Both of these things will happen together, one cant happen without the other, so “AND” case, so we multiply these terms

if they go alone, remaining answer can be found by f(n-1)

Now going alone and going with a partner are 2 different scenarios and cannot happen together, so its a OR case, so we add these terms.

Is it clear now?