arjunsridhar84 wrote:
Hi Bunuel - i didnt understand how yangsta arrived at 1*2*1*1 for all incorrect or for that matter 1*1*1*1 for one incorrect and so on... i didnt quite follow this logic.
kindly explain
Counting 1 correct: 4C1=4, choosing which letter will be put in correct envelope. (Let's assume A letter was put in correct envelope).
Then 3 letters (BCD) and 3 envelopes (BCD) are left. # of ways to put them incorrectly is 2:
Envelopes: B-C-DLetters: C-D-B
OR: D-B-C
So total # of ways one letter will be put into the envelope with its correct address is: 4C1*2=8. As total # of ways to distribute 4 letter in 4 envelopes is 4!=24, probability P(C=1)=8/24.
Counting 2 correct: 4C2=6, choosing which 2 letter will be put in correct envelope. (Let's assume A and B letter were put in correct envelopes).
Then 2 letters (CD) and 2 envelopes (CD) are left. # of ways to put them incorrectly is 1:
Envelopes: C-DLetters: D-C
So total # of ways two letters will be put into the envelope with its correct address is: 4C2*1=6. As total # of ways to distribute 4 letter in 4 envelopes is 4!=24, probability P(C=2)=6/24.
Counting 3 correct: if three letters will be put in correct envelopes, then the fourth one also gets its correct envelope. So there is no way we can put exactly 3 letters in correct envelopes --> P(C=3)=0
Counting 4 correct: there are 4!=24 ways to distribute 4 letters in 4 envelopes and obviously only one is when all letters get their correct envelopes. P(C=4)=1/24.
Counting all incorrect, or 0 correct:P(all incorrect)=1-(1 correct)-(2 correct)-(3 correct)-(4 correct)=1-8/24-6/24-0-1/24=9/24.
ichha148 wrote:
A. That no letter will be put into the envelope with its correct address?
9/24
B. That all letters will be put into the envelope with its correct address?
1/24
I understand that correct answer is 9/24 , however my question is should not the B. That all letters will be put into the envelope with its correct address? is opposite of no letter will be put into the envelope with its correct address?
So , should not the result be 1-1/24 = 23/24
Can some one please explain me why this is not 23/24 and when 23/24 is applicable
Opposite of "all letters in correct envelopes" (= 1-1/24 = 23/24), is: "at least one in wrong envelope" = "3 correct" (=0) + "2 correct" (=6/24) + "1 correct" (=8/24) + "0 correct, option A" (=9/24) --> \(1-\frac{1}{24}=\frac{23}{24}=0+\frac{6}{24}+\frac{8}{24}+\frac{9}{24}=\frac{23}{24}\).
Hope it's clear.
I have a basic question. In this case we have 4 letters and 4 envelopes. So lets say the letters are L1-L4 and envelopes are E1-E4.. Now there are 4! combinations between the two.. I am trying to understand how we arrive at that.. If I use the logic that I select 1 letter from the 4 letters and 1 envelope from the 4 envelopes and pair them together we get 4C1 x 4C1 = 16 combinations.. Where is my thinking wrong? I understand 4! as we can select one of the 4 for the first envelope... 4x3x2x1=4!, but where is 16 missing the combinations? Thanks