Permutations starting with a specific letter

Question

Ok, this is a homework question and I think I've resolved it but I want to bounce it off you guys.

I have a $6$ letter word with no repeated letters. I need to calculate how many $3$ letter words can be formed from this word and all must start with the letter $W$.

This is what I've got as the answer:

$$P((n-1),r) = P(6-1,3) = P(5,3) = \frac{5!}{(5-3)!} = \frac{5!}{2!} = 5·4·3 = 60$$

Am I in the ball park?

I took out 1 as there is 1 letter that has to be in the word - W. So I was trying to work out the left over permutations. — Moira, Apr 23 '16 at 13:21
With fewer symbols: The second letter of your three-letter word can be chosen in $5$ ways. For every such choice, the third letter of your word can be chosen in $4$ ways, for a total of $(5)(4)$. — André Nicolas, Apr 23 '16 at 14:22

score 1 · Answer 1 · answered Apr 23 '16 at 13:24

1

So, you're close, but not quite there. The answer is $20$ not $60$, and if you want to see why, check under the spoiler

There are only two letters that you have a choice for, because the third letter is a W. Your word is of the form "W __ __" so the answer has $r=2$ not $r=3$. Besides that you're right.

answered Apr 23 '16 at 13:24

Stella Biderman

31,155

1

Thanks Stella. I wanted to make sure I was in the ball park. I see what you mean about r. :) I've updated it and now I fully understand how this works. Onto the next question of my homework! :D – Moira Apr 23 '16 at 13:26
@Moira you should consider pressing the check mark next to this answer to" accept" it – Stella Biderman Apr 24 '16 at 03:24

Permutations starting with a specific letter

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