I will form a 3 letter code word using only the first 12 letters of the alphabet allowing no letter to be used
I will form a 3 letter code word using only the first 12 letters of the alphabet allowing no letter to be used more than once in any code word. If I select a code word at random, find the probability that the code word begins with the letter C and ends with a vowel.
the probability of the first letter being a c is: 1/12…
there are only 3 vowels in the first 12 letters (a, e, i) so there is a 3/11 chance that a vowel will be in the last one (11 because youve already selected the c from before) the chance of the middle letter being anything is 1, so multiply
1/12 * 3/11 * 1
and you get
3/132
or
1/44
another way to look at this is that there is only one c in the first 12 letters, theres only 3 vowels in the first 12 letters, and there is only 10 letters THAT ARE UNSELECTED in the first 12 letters, so do
3 * 10 * 1
now… supposedly, there were no rules at all, and the code can be anything, the first letter could be 12 letters, the second letter could be 11 letters (after selecting the first letter) and the 3rd letter can be 10 letters (after selecting the first 2 letters) so
12 * 11 * 10
no the probability is
3 * 10 * 1
————-
12*11*10
if you rearrange everything, you can see we go back to
1/12 * 3/11 * 10/10 (or 1)
ABC Song
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