SATHEE: Permutations And Combinations Question 369

Permutations And Combinations Question 369

Question: Ravish writes letters to his five friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?

Options:

A) 109

B) 118

C) 119

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Required number of ways $ \sum\limits _{r=2}^{5}{^{5}{C _{5-r}}D(r)} $ $ =\sum\limits _{r=2}^{5}{\frac{5!}{r!(5-r)!}r!{ 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+…+\frac{{{(-1)}^{r}}}{r!} }} $ $ =10+20+(60-20+5)+(60-20+5-1) $ $ =10+20+45+44=119 $

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Permutations And Combinations Question 369

Question: Ravish writes letters to his five friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?

Options:

Answer:

Solution:

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