- #1

MinusTheBear

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## Homework Statement

I have two homework problems that seem similar, but I'm trying to understand another approach to the problem.

**Question 1:**One hundred tickets, numbered 1, 2, 3,..., 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if the people holding tickets 19 and 47 both win prizes?

**Question 2:**The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain exactly two vowels.

## Homework Equations

## The Attempt at a Solution

Attempt on solution 1: C(4,2) * 2 * 1 * 98 * 97

Attempt on solution 2: C(6,2) * 5^2 * 21^4

So, I got the same answer as the back of the book, but the back shows the solution for question 1 as C(4,1) * C(3,1) * 98 * 97.

I'm not sure I understand where they are getting the C(4,1), C(3,1) because using a similar approach on the second question doesn't work. IE C(6,1) * C(5,1) * 21^4. I see that the C(4,1) and C(3,1) is eliminating the positions available.

**But why doesn't this work similarly with question 2? Is it because the letters can be repeated?**

Thanks.