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

Step-by-step solution

Let n=4 be number of envelopes in which number letters goes into envelope meant for it. Then, the number of ways =4 !- _ k=1 ^4 ^4 C_k aligned & [ required number of ways =n !- _ k=1 ^n ^n C_k ] = & 24- [ ^4 C₁+ ^4 C₂+ ^4 C₃+ ^4 C₄ ] = & 24-[4+6+4+1]=24-15=9 aligned Hence, required number of ways =9