6th Grade Math Textbook, Fundamentals

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

1 10 45 120 210 252 210 120 45 10 1

1 11 55 165 330 462 462 330 165 55 11 1

1 12 66 220 495 792 924 792 495 220 66 12 1

1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1

1 Row 0

Row 1

Row 2

Row 3

Row 4

Row 5

Row 6

Row 7

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1.Sawyer has six pairs of shorts. He wants to take four pairs on vacation.

Find the number of combinations for four pair of shorts.

2.An ice-cream parlor offers 10 flavors. Akila wants to order a sundae

with three different flavors of ice cream. How many different three-scoop

sundaes are possible?

page 391 for exercise sets.

Enrichment:

Pascal’s Triangle

Objective To use Pascal’s Triangle to find numbers of combinations

The pattern of numbers at the right is part of.
(The full triangle continues with more rows.) The triangle is
named after the French mathematician Blaise Pascal, who lived
from 1623–1662.

Pascal’s Triangle has many interesting patterns.

Here are just a couple. See if you can find others.

• The numbers on the edges are 1s. Each of the other
  numbers is the sum of the two numbers above it.
  For example, the number 10 in Row 5 is the sum
  of 4 and 6 above it.


• The sums of the numbers in each row are
  successive powers of 2.
  Row 0: 1  20
  Row 1: 1  1  2  21
  Row 2: 1  2  1  4  22
  Row 3: 1  3  3  1  8  23 and so on.

You can use Pascal’s Triangle to find numbers of combinations. For example,

suppose you have three extra tickets to a concert, and seven of your friends

want to go with you. How many different combinations of three friends are possible?

To find the number of combinations of 7 things taken 3 at a time, use Pascal’s Triangle.

• Choose the row that corresponds to the number
  of items you are choosing from. In this case, choose
  Row 7. (Notice Row 7 is actually the eighth row.)


• The first number, 1, is the number of combinations
  of 7 things taken 0 at a time. The second number, 7,
  is the number of combinations of 7 things taken 1 at
  a time, and so on.


• You want to find the number of combinations
  of 7 things taken 3 at a time. This is the fourth
  number in the row, which is 35.

There are 35 possible combinations of three friends.

Pascal’s Triangle

1 7 21 35 35 21 7 1

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7

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Row 7