Question

A father purchases dress for his three daughters. The dresses are of same colour but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress.

• A. \(\frac{2}{3}\)
• B. \(\frac{1}{3}\)
• C. \(\frac{2}{6}\)
• D. \(\frac{2}{9}\)

Answer 1

The Correct Option is B

Probability of Derangement

The total number of ways in which the three daughters can choose their dresses is: 

\[ 3! = 6 \]

Step 1: Finding Favorable Outcomes

To determine the number of ways in which none of the daughters chooses her own dress, we use the concept of derangements.

The number of derangements of 3 items is:

\[ !3 = 2 \]

Step 2: Calculating Probability

The probability that none of the daughters chooses her own dress is:

\[ \frac{2}{6} = \frac{1}{3} \]

Final Answer

Thus, the probability that all three daughters do not choose their own dress is \(\frac{1}{3}\).