Question

In how many ways $6$ letters can be placed in $6$ envelope such that:

At least $4$ letters are placed in correct envelopes

• A. $16$
• B. $20$
• C. $24$
• D. $25$

Answer 1

The correct option is A $16$

When $4$ letters are in correct envelopes, then there is only on possible way in which the remaining two is using envelopes. This is same as selecting four out of side envelopes$={}^6{C}_4={}^6{C}_{6-4}={}^6{C}_2=15$

There are $15$ ways in which exactly $4$ envelops contain correct letters.

It is not possible to place $5$ letters in envelopes correctly because, the $6^{th}$ letter fits in the correct envelope as well.

Hence there is the only way to place all letters in the correct envelopes.

Total number of ways of placing atleast $4$ letters in correct envelopes

$=15+1=16$ ways.