There are three families in which 2 families has 3 members each and third family has 4 members. They are arranged in a line. then probability that members of same family are together is:
Answers
It has given that, in three families, two families have 3 members each and third family has 4 members. they are arranged in a line.
To find : the probability that members of same family are together is
solution : total members in three family = no of members of first two families + no of members of 3rd family.
= 3 + 3 + 4 = 10
so total arrangements of members, n(S) = 10!
in first family, there are three members. so total arrangements in three members = 3!
similarly total arrangements in three members of 2nd family = 3!
and no of arrangements in four members of 3rd family = 4!
and all three families arrange in 3! ways
so favourable cases, n(E) = 3! × 3! × 3! × 4!
now probability = n(E)/n(S) = 3 × 3! × 3! × 4!/10!
= (6 × 6 × 6 × 4!)/(10 × 9 × 8 × 7 × 6 × 5 × 4!)
= 1/(5 × 4 × 7 × 5)
= 1/700
Therefore the probability is 1/700 I.e, option (1) is correct choice.