A photographer is lining up 5 family members in a line for a picture.
Let the mother be M, father be F, and the children be A,B,C
How many different lineups can there be if the mother and
father stand by side?
Number of permutations of 4 things {(MF),A,B,C}
plus
Number of permutations of 4 things {(FM),A,B,C}
Answer: 4P4 + 4P4 = 4! + 4! = 2*4! = 2*24 = 48
If the mother and father are on either end?
Number of permutations of MF{A,B,C}
plus
Number of permutations of FM{A,B,C}
plus
Number of permutations of {A,B,C}MF
plus
Number of permutations of {A,B,C}FM
Each is permutations of 3 things:
Answer = 4(3P3) = 4(3!) = 4(6)=24 ways
The father is on the left and the mother is on the right?
Number of permutations of F{A,B,C}M
Answer: 3P3 = 3! = 6 ways.
Edwin