Question

4 friends put their car keys on table when they leave they picked up their keys at what is the probability that no person picks the right key

Answer 1

hey the answer is 1/4 .

Answer 2

Given: 4 friends put their car keys on table when they leave they picked up their keys.

To find: The probability that no person picks the right key.

Solution:

The total number of ways to pick up the keys can be written as follows.

$4! = 24$

The number of ways in which the first person picks up his own keys is

$^{4}C_{1} = 4$

The number of ways in which the second person picks up his own keys is

$^{4}C_{2} = 6$

The number of ways in which the third person picks up his own keys is

$^{4}C_{3} = 4$

The number of ways in which the fourth person picks up his own keys is

$^{4}C_{4} = 1$

Thus, the number of ways in which no person picks up his own keys can be calculated as shown below.

$24 - (4+6+4+1) = 24-15$

                                $=9$

Hence, the probability that no person picks up his own keys is

$P(E) = \frac{9}{24}$

         $=\frac{3}{8}$

Therefore, the probability that no person picks the right key is 3/8.