Pascal's Triangle

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1. The row of Pascal’s Triangle containing just two ones is normally referred to as row 1. The solitary one at the top of the triangle is row zero. Row two contains the numbers 1,2 and 1 in that order.

What is the number in row 5 next to the one?

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2. What is the sum of all the numbers in row 4?

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3. What is the sum of all the numbers in rows 0 to 6?

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4. The sum of the numbers in a particular row add up to \( x \). What do the numbers in the row below this row add up to?

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5. A calculator can be used to find any number in Pascal’s Triangle given the row number and the position of the number from the left of the row [noting that the first number in a row is in position zero]. Click the HELP tab above for information about using a calculator for the following questions:

Use a calculator to find the number in row 20, position 4.

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6. Use a calculator to find the number in row 41, position 5.

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7. The number in row 27, position 3 can be represented as \( \begin{pmatrix}27\\3\\ \end{pmatrix} \)

Find \( \begin{pmatrix}27\\3\\ \end{pmatrix} \)

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8. Find \( \begin{pmatrix}53\\50\\ \end{pmatrix} \)

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9. The calculation \( \begin{pmatrix}5\\3\\ \end{pmatrix} \) can be written as 5C3 (pronounced five choose three) and can be used to find the number ways of choosing three items from five.

How many ways are there of choosing 2 players from a team of 11?

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10. How many different ways can seven cakes be chosen from a tray containing ten cakes?

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Striped Sweets

Striped Sweets

Colour the sweet wrappers so that no two are the same. A multi-level activity designed to encourage a systematic strategy for finding all of the different permutations.

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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.

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Description of Levels

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Level 1 - Fill in the numbers on a blank triangular grid

Level 2 - Colour in the even numbers to produce a surprising pattern

Level 3 - Colour in the multiples of 3 to produce a surprising pattern

Level 4 - Colour in the remainders when dividing by four in different colours

Level 5 - Colour in sets of six connected hexagons that have given sums

Level 6 - Use a calculator to find particularly large numbers from Pascal's Triangle

Level 7 - Learn about the binomial theorem by answering questions about expanding brackets

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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Using a Calculator

The function to work out a number in Pascal's Triangle appears as nCr where:

nCr Formula nCr button on calculator

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