Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter , she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only I ( ONE) letter will be put into the envelope with its correct address ? ( got this teaser in GMAT PREP)
Letters can be arranged in 4 ! Ways , that is, 4×3 x 2×1 ways = 24 ways
(Since letter can be put into first envelope in 4 ways, in second envelope letter can be put in 3 ways, letter can be put into third envelope in 2 ways, letter can be put into fourth envelope in 1 way)
Probability that only one letter will be put into the envelope with its correct Address = 4/24 =1/6
( Four possibilities are:
1. first letter will be put into the envelope with it’s Correct address and rest three are incorrect
2. Second letter will be put into the envelope with its Correct address and rest three are incorrect
3. Third letter will be put into the envelope with its correct address and rest three are incorrect
4. Fourth letter will be put into the envelope with its correct address and rest three are incorrect )
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