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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Probability

NDA 2011 · Mathematics · Probability

There are 4 letters and 4 directed envelopes. These 4 letters are...

There are 4 letters and 4 directed envelopes. These 4 letters are randomly inserted into the 4 envelopes. What is the probability that the letters are inserted into the corresponding envelopes?

Options

  1. A11/1211 / 12
  2. B23/2423 / 24
  3. C1/241 / 24
  4. DNone of these

Correct answer

C. 1/241 / 24

Step-by-step solution

Four letters can be placed in 4 envelops in 4 ! ways whereas there is only one way of placingthemintheirrightenvelops.Sothattheprobabilitythatallthelettersareplacedplacing them in their right envelops. So that the probability that all the letters are placed in the right envelops =14! ways =14×3×2=124.\begin{aligned} & \text{ in the right envelops }=\frac{1}{4!} \text{ ways } \\ & \qquad=\frac{1}{4 \times 3 \times 2}=\frac{1}{24}. \end{aligned}$$
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