I have tried using mutual inclusion - exclusion here but it seems to not work here . Can anyone point out why ? Here’s what i did
N(L,I,A,C not in their place) = N(total permutation) – N(either L or I or A or C is in it’s own position)
For finding N (I or L or A or C ) i have used mutual inclusion exclusion in the following way
= N (I in place ) + N(L in place) + N(A in place) + N(C in place) – N (L and A in place) – N(L and I in place) – N(L and C in place) – N(A and C in place) – N(A and I in place) – N(I and C in place) + N( L , I , A in place) + N(L , A , C in place) + N(I , A , C in place) + N(L , I , C in place) – N(L , I , A , C in place)
= 4!/2! + 3! + 4!/2! + 4!/2! – 2! – 2! – 2! – 3!/2! – 3!/2! – 3!/2! + 1 + 1+ 1 + 1 – 1
= 30
So N (L,I,A,C no in place) = 5!/2! – 30 = 60 – 30 = 30
Can anyone point out where my understanding went wrong ?