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1. What is the sum of the first 7 terms in diagonal 10 of the Pascal's Triangle? 2. What is the sum of the terms in row # 14 of the Pascal's Triangle? 3. Write the first 4 terms in row # 17 of Pascal's Triangle?

1. What is the sum of the first 7 terms in diagonal 10 of the Pascal's Triangle? 2. What is the sum of the terms in row # 14 of the Pascal's Triangle? 3. Write the first 4 terms in row # 17 of Pascal's Triangle?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. What is the sum of the first 7 terms in diagonal 10 of the Pascal's Triangle? 2. What is the sum of the terms in row # 14 of the Pascal's Triangle? 3. Write the first 4 terms in row # 17 of Pascal's Triangle? 4. If you know that a term in Pascal's Triangle can be represented by 20C15, what row # and position is this term in? 5. You are decorating a chocolate cupcake to give to your friend, and you can choose from any of the following decorations: icing, sprinkles, gummy bears, sour keys, and peanuts. You can choose any number of decorations that you can, but you know that you friend will also be happy if there are no decorations on the cupcake. How many ways can you prepare this cupcake? 6. How many ways can you arrange the letters in the word ETHIOPIA if: a. There are no restrictions? b. The consonants must remain in the same order? c. The i's must not be together? d. The T & H must remain in the same spot?
Transcribed Image Text:1. What is the sum of the first 7 terms in diagonal 10 of the Pascal's Triangle? 2. What is the sum of the terms in row # 14 of the Pascal's Triangle? 3. Write the first 4 terms in row # 17 of Pascal's Triangle? 4. If you know that a term in Pascal's Triangle can be represented by 20C15, what row # and position is this term in? 5. You are decorating a chocolate cupcake to give to your friend, and you can choose from any of the following decorations: icing, sprinkles, gummy bears, sour keys, and peanuts. You can choose any number of decorations that you can, but you know that you friend will also be happy if there are no decorations on the cupcake. How many ways can you prepare this cupcake? 6. How many ways can you arrange the letters in the word ETHIOPIA if: a. There are no restrictions? b. The consonants must remain in the same order? c. The i's must not be together? d. The T & H must remain in the same spot?
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