Hello,

please try to solve these questions.

m777

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- Dec 29th 2006, 03:05 AMm777eudlidean algorithm,permutation.....
Hello,

please try to solve these questions.

m777 - Dec 29th 2006, 04:39 AMtopsquark
Use the Euclidean Algorithm to find gcd(190, 34).

Given two integers a and b (a > b) and the equation:

where q and r are some integers (r < b).

The Euclidean Algorithm states that

So start with a = 190 and b = 34.

By simple division we can find that:

Thus .

Repeating this process on gcd(34, 20):

So .

Continuing:

.

.

Now, this means that 2 is a divisor of 6, so we are done:

.

Thus .

-Dan - Dec 29th 2006, 04:52 AMgalactus
For #1b:

Using the definition of factorial, we can cancel terms in the denomiantors:

Do the same for the other and we get

We have:

Which gives:

Which gives :

One of these is your answer. I would think it's 9. - Dec 29th 2006, 06:45 AMSoroban
Hello, m777!

Quote:

1(a) Use the Euclidean Algorithm to find

I was taught this way . . .

[1] Divide the larger by the smaller; note the remainder.

[2] Divide the remainder into the divisor; note the remainder.

[3] Repeat step 2 until the remainder is 0.

[4] The is the last divisor.Code:`5 1 1 2 3`

------ ---- ---- ---- ---

34 ) 190 20 ) 34 14 ) 20 6 ) 14 2 ) 6

170 20 14 12 ↑ 6

--- --- --- --- --

20 14 6 2 0

Therefore: .

Quote:

1(b) Find if:

We have: .

Divide by

The quadratic factors: .

. . and has two solutions: .

Since must be positive, the answer is: .

Quote:

2. A computer access code consists of from one to three letters

. . of the English alphabet with repetition allowed.

How many different code words are possible?

Since each code letter has 26 choices,

. . there are: . possible code words.

Quote:

3(a) A box contains 10 different colored light bulbs.

Find the number of ordered samples of size 3 with replacement.

The first can be any of the 10 bulbs.

The second can be any of the 10 bulbs.

The third can be any of the 10 bulbs.

There are: . possible ordered samples.

Quote:

3(b) How many possible outcomes are there when a fair coin is tossed three times?

The first toss has 2 possible outcomes (Heads or Tails).

The second toss has 2 possible outcomes.

The third toss has 2 possible outcomes.

There are: . possible outcomes.

Quote:

4. How many 2-permutations are there of ? .Write them all.

There are: . permutations.

They are: .

- Dec 29th 2006, 08:08 AMm777excellent.........
Hello soroban,

you are genius.

from

m777