discrete math prob

 Essay in discrete math prob

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1- An office building consists of 27 floors and has thirty seven offices on each of your floor. How many office buildings are inside the building? Option:

Total number of offices can be 27 2. 37 =999

2- A particular brand of clothing comes in 12 colors, has a men version and a girl version, andcomes in three sizes for each sex. Just how many different types of this shirt are made? Solution:

Using product secret, we have 12×2×3 = 72 various kinds of this clothing.

3. Make use of a tree diagram to find the number of bit strings of span four without having three successive 0s.

Terrain:

4. Just how many ways is there to arrange the letters a, b, c, and d such that a is certainly not followed quickly by w? With " a" inside the 1st situation: �

       

acbd�

       

acdb�

       

adbc�

       

adcb�

With " a" in the second position: �

       

bacd�

       

badc�

       

cadb�

       

dacb�

With " a" in the 3rd position: �

       

bcad�

       

bdac�

       

cbad�

       

dbac�

With " a" in the next position: �

       

bcda�

       

bdca�

       

cbda�

       

cdba�

       

dbca�

       

dcba

There are 18 ways

5. How many different plates can be made out of one letter followed by a single number? Terrain:

There are 21 choices of characters. Each of these 26 letters may be followed by certainly one of 10 Diverse digits--0, 1, 2, 3, 4, 5, 6, six, 8, on the lookout for.

Therefore you will find 26 x1 0 sama dengan 260 several plates that can be made 6. How various license plates can be manufactured using either two or three characters followed by either two or three digits? � Sol:

For two albhabets, there are dua puluh enam choices for the first letter and 26 for the 2nd. For the two letters, you will discover 10 selections for the 1st letter and 10 for the second. �

That's 26²(10²) = 67600�

For two albhabets followed by 3 numbers, multiply by 12 again: �

26²(10²)(10) = 676000�

For 3 letters, 26²(26)�

With two numbers, 26²(26)(10²) = 1757600�

With 3 numbers, 26²(26)(10²)(10) = 17576000�

Adding them up�

67600 + 676000 + 1757600 + 17576000 = 20077200...