Question

There are $5$ letters and $5$ addressed envelopes.The number of ways in which the letters can be placed in the envelopes so that none of them goes into the right envelope is

• A. $22$
• B. $44$
• C. $120$
• D. $119$

Answer 1

Answer: (B)

$44$

The number of ways to put $5$ letters in $5$ addressed envelop so that all are in wrong envelopes
$=$The number of ways without restriction

$-$ The number of ways in which all are in correct envelope

$-$ The number of ways in which $1$ letter is in correct envelope

$-$ the number of ways in which $2$ letters are in correct envelope

$-$ The number of ways in which $3$ letter are in correct envelopes

$-$ the number of ways in which $4$ letter are in correct envelopes
$=5!-1{-}^5{C}_1\times 9{-}^5{C}_2\times 2{-}^5{C}_3\times 1-0=120-1-45-20-10-0=44$