Discussion Forum

The number of ways  in which four letters can be put in four addressed envelops so that no letter goes  into envelope  meant for it is

Answer:

Explanation:

Let n=4 be number of envelopes in which number letters goes into envelope meants for it

Then, the number of ways =4!= $\sum_{k=1}^{4}{^{4}}{C}_{k}$

[ $\because$ required number of ways = n!= $\sum_{k=1}^{n}{^{n}}{C}_{k}$

   =$24-[^{4}C_{1}+^{4}C_{2}+^{4}C_{3}+^{4}C_{4}]$

  =24-[4+6+4+1]=24-15=9

  Hence , required number of ways =9