A family of 2 parents, 4 children, and 1 grandparent are sitting in a single row

Question

A family of 2 parents, 4 children, and 1 grandparent are sitting in a single row on an airplane takes up the whole row on the airplane a) How many different ways can the family be arranged in the row? (2 points) b) What is the probability that a parent is at each end of the row? (3 points) l14, 0 Considering only whether a family mémber is a parent, child, or grandparent, in how many ways can the family be arranged? (3 points) c) d) Considering only whether a family member is a parent, child, or grandparent, what is the probability that the parents are sitting together? (3 points).

Explanation / Answer

a)

here multinomial coefficient can be used if 2 parents are identical and 4 grandparents are identical

multinomial is used when objects are identical ; like 2 green marbles,4 blue marbles ; 1 red marbles

as same color marble are indistinguishable you can use multinomial

this should be simply 7! =5040

b)

both parents are ends ; therefore they can interchange in 2 ways ; whilre we need to arrange middle 5 persons ; number of ways =2*5! =240

hence probability =240/5040=0.0476

c)

here as we are considering that both parents are indistingushable as well 4 grandparents

hence number of ways =7!/(1!*2!*4!)=105

d)

as parents are sitting together they can be considered 1 unit ; hence number of ways =6!/(1!*1!*4!)

=30

probability =30/105=0.2857

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