Question

K's family consists of a grandfather. w sons and daughters and 2 grandchildren. They are to be seated in a raw for dinner The grandchildren wish to occupy the 'n' seats at each end and grandfather refuses to have a grandchild on either side of him, In How many ways can k's family be made to sit?

A. (2nl)(m+1)l

B. (2nl)(m-1)l

C. (2ml)(nl)

D. (2nl)(ml)(m-1)​

Answer 1

The number of ways of arranging the grand children at each end's (2n)!

Sons and daughter can be occupies by m!

While grandfather will occupy the remaining seat in middle i.e. (m−1).

Note! After grandfather only we shall arrange son and daughter

∴ Total ways=2n!×m!(m−1)

Hence the answer is (2n)!m!(m−1).