Question

If four letters are placed into 4 addressed envelopes at random, the probability that all the four letters will go wrong is

• A. $\frac{5}{24}$
• B. $\frac{7}{24}$
• C. $\frac{9}{24}$
• D. $\frac{11}{24}$

Answer 1

Answer: (C)

$\frac{9}{24}$

total ways of placing $=4!=24$
no. of ways such that 3 correct and 1 wrong $=0$
no. of ways such that all 4 are correct $=1$
no. of ways such that 2 correct and 2 wrong = $4C_2\ast 1=6$
no. of ways such that 1 correct and 3 wrong $=4C_3\ast 2=8$
no. of ways such that all 4 are wrong =$24-6-8-1=9$
probabilty =$9/24$