Snow White and the Seven Dwarves

By: Lucas Adams, Suo Ryu

In 1930s, Walt Disney made the story of the Snow Whites into a cartoon, using 20 different colours of ink (at that time, the cartoons were drawn by hands) He could use variety of 20 colours to make magnificent cartoons.

-20 colours, all different-at least one colour should be used (there is NO cartoon with NO inks!!! Therefore, you have to subtract 1 for your null set)

Therefore, I knew that there were:

220-1 = 1048575 choices of drawing my cartoon!!!!

Once upon a time, in a land far far away,there was a queen. One day, she pricked her finger on her needle and three drops of blood fell on the snow on her ebony window frame. As she looked at the blood on the snow, she said she wished to have a daughter that had skin white as snow, lips red as

blood, and hair black as ebony. And of course, she gave birth to a daughter who looked just like that. She died after the child was born. They named her

Princess Snow White

There were many outcomes besides having a black hair, red lips and white skin. She could have had

either brown or blonde hair, orange or pink lips due to the genetics. There was

White Skin

Blonde HairBrown Hair

Black Hair

Red Lips

Orange Lips

Pink Lips

Red Lips

Orange Lips

Pink Lips

Red Lips

Orange Lips

Pink Lips

1 x 3 x 3 = 9 possible outcomes of genes.

After the death of the queen, the King got married with another woman. The new queen was very vain.

Everyday she would look in the mirror, saying, “Mirror mirror on the wall, who is the most beautiful of all?”

and the mirror mentioned Snow White. She got jealous and ordered the huntsman to kill her in the

forest, but he was unable to kill her because she was a child, so he just let Snow White flee.

In the forest, Snow White finds a cottage owned by seven dwarves. They take pity on her and let her stay

if she keeps the house clean and organized. The Seven Dwarves are named:

Doc Sneezy Sleepy Grumpy

Dopey BashfulHappy

That weekend, they all went out for lunch. They first decided to have Subways or McDonalds for lunch, and then a cup of coffee from Starbucks, Tim Hortons, or Second Cup. And to top it all off, they had the choice

to have ice creams or pies. Dopey did not want to have McDonalds and pies

together , and Grumpy wanted Subway sandwiches with Tim Hortons Coffee.

All lunch choices = 2 x 3 x 2 = 12Mcdonalds and Pies Together = 1x3x1 = 3

Dopey had 12-3 = 9 choices for lunch.

Having Subway & Tim Hortons Together = 1x1x2 = 2

For Grumpy…

He had 2 choices for lunch.

After they got home, Snow White felt sick, so the dwarves decided they would help out with the

chores. 4 of the dwarves did the dishes, 3 dwarves mopped, and 5 dwarves recycled. Happy did all three since he was overly energetic. Sleepy fell asleep, not helping them. 3 of the dwarves did both dishes and

recycling. 2 of the dwarves did the dishes and mopping, and 2 of the dwarves did the mopping and

recycling.

Snow White wanted to know how many dwarves only recycled, so she could give them more chores to do.

0

0

1

S

1

1 1

2

1

D R

M

It was SNEEZY !!! He was feeling lazy so he only recycled.

Snow White felt thankful for the dwarves’ help and hospitality, so she made freshly-squeezed juice, but there were only 3 glasses, so it would be first come,

first serve.

There was

7P3 = 7! / (7-3)!=7x6x5=210

So, there was 210 ways 3 dwarves from 7 could have had the juice.

Dopey woke up that morning and looked in the mirror. He looked so “dopey” so he decided it was time for a change. He went to the closet and displayed all the

clothing he had in the closet on the bed. But they were each identical.

There was-2 hats-4 shirts-3 pairs of pants-identical

Therefore…9! / 2!4!3! = 1260

There was-2 hats-4 shirts-3 pairs of pants-identical

Therefore…9! / 2!4!3! = 1260

9 total

There were 1260 ways of displaying the clothing.

Meanwhile, the Queen was asking the mirror again who was the most beautiful of them all. And AGAIN!!! The mirror answered “Snow White.” This made the Queen

infuriated.

Snow white is still pretty

LOL

She immediately set out to rid the world of Snow White. She decided to disguise herself as a farmer’s

wife and poison snow white with apples.

She picked 4 apples from a basket of 8 apples (consider they are all different). Then she made the 4

apples poisonous. Therefore…

4 Apples out of 8-All Different

Therefore… using combination,

8C4 = 70 ways

The queen had 70 ways of choosing 4 apples out of 8.

The Queen then, disguised herself and set out to find Snow White and the seven dwarves. These are the

path that she could take. The Queen wanted to eliminate Snow White fast so she never went

backwards..

JUICY !!!

The dwarves’ place was 4 blocks east, 4 blocks south from the castle

Therefore…

1 1 1 1 1

1

1

1

1

2 3 4 5

3

4

5

6

10

15

14

29 34

There were 34 possible routes that the Queen could take.

Q

D

Meanwhile, the unsuspicious Snow White decided she wanted some cookies for snack. The cookie jar

contained 3 raisin cookies, 2 chocolate chip cookies, 1 peanut butter cookie, and 4 almond cookies. Since she

was so hungry, she had at least one cookie.

-3 raisin, 2 chocolate, 1 peanut, and 4 almonds-choosing at least one

= (p+1)(q+1)(r+1)… - 1= (3+1)(2+1)(1+1)(4+1)-1=119

-3 raisin, 2 chocolate, 1 peanut, and 4 almonds-choosing at least one

= (p+1)(q+1)(r+1)… - 1= (3+1)(2+1)(1+1)(4+1)-1=119

There were 119 ways for Snow White for choosing at least one cookie.

The Queen arrived at the cottage, disguised as a farmer’s wife to deceive Snow White and put an end to

her. The dwarves were out that day, so Snow White answered the door when the Queen knocked. The Queen

offered Snow White the apples, saying that they had farmed too many. Snow White being and nice and

generous invited her in.

Out of 8 apples, the Queen ate 2 of the good apples, and gave 2 apples to Snow White. The queen made sure that

Snow White chose at least one poisonous apple.Therefore…

-8 apples (2 good apples because the queen ate 2, and 4 poisonous apples)

Therefore, there were 8+6 = 14 ways for the Queen to make sure that Snow White has at least one poisonous apples.

1) Choosing One poisonous apple

= 2C1 * 4C1

= 8

1) Choosing One poisonous apple

= 2C1 * 4C1

= 8

2) Choosing Two poisonous apples

= 4C2

= 6

2) Choosing Two poisonous apples

= 4C2

= 6

Indirect Method is also possible.

-All = 6C2 = 15-Don’t want = when she chooses no poisonous apple = 2C2 = 1

Therefore,Want = All- Don’t want = 15 – 1 = 14 ways

After eating the poisonous apple, Snow White collapsed and died.

The dwarves came back and were distraught to find Snow White dead on the floor. They put her in a glass

coffin and held a funeral for her.

During the funeral, a prince came by accidentally while he was lost in the woods. He was taken a back by Snow White’s beauty. He could not accept the death of such a

beautiful woman. So he convinced the dwarves to let him take her body. He then, kissed her, dislodging the

poisonous apple that was stuck in her throat. Snow White miraculously came back to life.

The prince asked Snow White if she can marry him. Snow White definitely wanted to say yes, but the

dwarves wanted to test him to see if he was worthy. Therefore, they gave him one math problem recently

theorized by Blaise Pascal.

(a+b)6

Fortunately, the prince was taught Data Management by Mrs. M. and could answer the question with ease.

= a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6

6

r=0(a+b)6 = ∑ 6Cr*a6-r*br

In general,

Therefore,

(x+y)n =

After the prince solved the question, the dwarves let him take Snow White. They lived happily ever after.

Before they got married, they threw a bachelor party

SHAKE THAT !!!

Overall Summary (Flow Chart of Combinatorics)

Is Order Important?

Permutation; CanSome objects be

selectedMore than once?

Combination ; Are you choosing

Exactly r objects?

Counting PrincipleAre some of the

Objects identical?

n! / a!b!c!

nPr = n! / (n-r)!

Could some of theObjects be identical?

Are some of theObjects identical?

Count individual cases

nCr = n! / (n-r)!r!

(p+1)(r+1)…-1

2n or 2n-1 if youDon’t want the null set

-Blue box indicates yes

-Pink box indicates no

- The End -