Thread: [SOLVED] permutations problem

1. [SOLVED] permutations problem

Hi,
Can any body will help me this?

1) how many words of 10 letters can be formed using english alphabets?
2) same question with no letter repeated?
3)How many words of length 8 can you form, where the first letter
is the same as the last letter?
4)How many words of length 8 can you form, which contain exactly
one vowel

Proposed solution

1) 26^10
2)26!/(26-10)!
3) 26^7
4)?
(26x25x24x23x22x21x20) + 5

2. Originally Posted by baz
1) how many words of 10 letters can be formed using english alphabets?
2) same question with no letter repeated?
3)How many words of length 8 can you form, where the first letter is the same as the last letter?
4)How many words of length 8 can you form, which contain exactly one vowel
Proposed solution
1) 26^10
2)26!/(26-10)!
3) 26^7
4)?
(26x25x24x23x22x21x20) + 5
The first three are correct.
For number 4. Choose one vowel and one place to put it.
There are 21 other letters and seven places left.
So what is that product?

3. so answer for fifth one would be 26^7 +5.

4. Originally Posted by baz
so answer for fifth one would be 26^7 +5.
The answer to the fourth question is $\displaystyle 5\cdot 8 \cdot(21)^7$.
I do not see a fifth question.