Question

There are four different letters and four addressed envelopes, in how many ways can the letter be put in the envelopes so atleast one letter goes into the correct envelope

• A. $15$
• B. $24$
• C. $9$
• D. None of these

Answer 1

The correct option is A $15$

It is given that at least one of it goes to correct addressed i.e, there is a possibility that either $2$ letters or $3$ letters or $4$ letters goes to correct addressed envelope.

$\therefore$ No of ways $1$ goes correct ${{}^{4}C}_1=4$

No of ways $2$ goes correct ${{}^{4}C}_2=6$

No of ways $3$ goes correct ${{}^{4}C}_3=4$

No of ways $4$ goes correct ${{}^{4}C}_4=1$

$\therefore$ Total no of ways $4+6+4+1=15.$

Hence, the answer is $15.$