There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is

Question

There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is (A) 8 (B) 9 (C) 16 (D) none of these

Tardigrade Admin · Accepted Answer

There is concept of derangement. The required number is 4![1 - (1/1!) + (1/2!) -(1/3!) + (1/4!)] = 9

Q. There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is

$8$

$9$

$16$

none of these

There is concept of derangement. The required number is
$4! [1 - \frac{1}{1 !} + \frac{1}{2 !} - \frac{1}{3 !} + \frac{1}{4 !}] = 9$

Q. There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is

8

9

16

none of these

There is concept of derangement. The required number is 4![1−1!1​+2!1​−3!1​+4!1​]=9

$8$

$9$

$16$

There is concept of derangement. The required number is
$4! [1 - \frac{1}{1 !} + \frac{1}{2 !} - \frac{1}{3 !} + \frac{1}{4 !}] = 9$