Five members of a family, husband, wife and three children are randoml

1.	Five members of a family, husband, wife and three children are randomly arranged in a row for a family photograph. Find the probability that the husband and wife are seated next to each other.
Answer» Five members of a family can be arranged in, n = ₅P⁵ = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways. A = Event that the husband and wife are seated next to each other. ∴ The favourable outcomes for the event A are obtained as follows: ∴ m = ₂P² × ₄P⁴ = 2! × 4! = 2 × 24 = 48 Hence, P(A) = \(\frac{m}{n} = \frac{48}{120} = \frac{2}{5}\)

Five members of a family, husband, wife and three children are randomly arranged in a row for a family photograph. Find the probability that the husband and wife are seated next to each other.

Answer»

Five members of a family can be arranged in,

n = ₅P⁵ = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways.

A = Event that the husband and wife are seated next to each other.

∴ The favourable outcomes for the event A are obtained as follows:

∴ m = ₂P² × ₄P⁴

= 2! × 4!

= 2 × 24 = 48

Hence, P(A) = \(\frac{m}{n} = \frac{48}{120} = \frac{2}{5}\)

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Five members of a family, husband, wife and three children are randomly arranged in a row for a family photograph. Find the probability that the husband and wife are seated next to each other.

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