how many different permutations of the letters A,B,C,D,E and F are there if each letter can be used once only? how many of these:
a. End in E D
b. begin with F and end with A
c. begin and end with a vowel?
Answers
Answered by
3
hi thank you for asking questions plz don't delete the answer because I am not copy to google..
How many permutations of the letters A, B, C, D, E, F, start with A?
Data structure is the most important topic for college placement.
Two approaches spring to mind. The first may seem long-winded, but may help if you are new to these problems and also gives the proportion of all permutations of these six letters that start with A as well as the number of permutations starting with A.
1 The total number of permutations of these six letters is 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
This is the case since:
* there is a choice of 6 letters for the first position
*once the first letter is chosen, you can choose any one of the remaining 5 letters for the second place
*there is then a choice of 4 letters for the third place, 3 for the fourth place, 2 for the fifth place and there is only 1 letter remaining to fill the last place each time.
As there will be an equal number of permutations starting with each of the six letters, one sixth of all the permutations start with A. There are 720/6 = 120 such permutations.
2 If you have already decided that the first letter is to be A, there are 5! permutations of the other five letters which follow the A. This gives 5! = 120 permutations of the 6 letters where A is the first letter.
Similar questions