four men two women and a child sit at a round table .find the nuber of ways of arranging the seven people if the child is seated ,
a.between the two women
b.between men
Answers
Answer:
a) 48
b)288
Step-by-step explanation:
Hi,
Given 4 men , 2 women and a child who has to be seated around a round
table.
In general n persons can be seated around a round table in (n-1)! ways
a) If child has to be seated between 2 women, let us consider all 3 as
together, then we need to arrange 4 men and this group at round table,
this can be done in 4! ways = 24 ways.
But 2 women can interchange their positions among themselves which can
be done in 2 ways, hence total number of ways would be 24 *2 = 48 ways
b) If child has to be seated between 2 men, let us choose any 2 men in
between whom child would be seated, so selected of 2 men could be done
in 4C2 ways = 6 ways, now all these 3 as group we can place 2 men + 2
women + group of 3 at round table in 4! ways = 24 ways, but these 2 men
can be interchange their positions among themselves which can be done in
2 ways, hence total number of ways would be 6*24 *2 = 288 ways
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