# Thread: Arrangements and Combinations application

1. ## Arrangements and Combinations application

I was having trouble with the following questions:

1)Find how many code words of three or four letters can be made from the letters of the word NUMBER:

a)if the letters can be re-used

2) A student has the choice of three mathematics subjects and four science subjects. In how many ways can they choose to study one mathematics and two science subjects?

2. Both these questions use the law of products.

The main idea is that if you want to count something that can be split into independent choices, then the total is the product of the number of possibilities for each independent choice.

For example, an outfit consists of a hat, a shirt, and pants. You have 3 hats, 4 shirts, and 2 pants. How many possible outfits are there? 3 x 4 x 2 = 24

So for each problem, first split it up into independent choices that have to be made. Try to work each problem a bit further in this direction.

Hint for 1a, the independent choices are what to pick for the first letter, what to pick for the second letter, etc.

3. Thanks. I am to solve these problems with help from Permutation and Combination knowledge, how would i interpret these problems into the basic forms of permutations and combinations?

4. Snowtea, i did what you said however the answer came out to be wrong.

5. Originally Posted by johnsy123
Thanks. I am to solve these problems with help from Permutation and Combination knowledge, how would i interpret these problems into the basic forms of permutations and combinations?
If the letters were not to be re-used, you would calculate permutations of 3 from 6 and 4 from 6.
Since the letters can be re-used, how many choices do you have for each letter...1st, 2nd, 3rd, 4th ?

6. Originally Posted by johnsy123
Snowtea, i did what you said however the answer came out to be wrong.
Which problem are you refering to? Also, show your work, so we can tell you exactly where the fault lies.