**"Permutations and combinations"**

## Grades 10 to 12 Two Aces

*By toni On 3 October, 2017 · Leave a Comment*

We have six cards, four Aces and the Jack of hearts and Queen of spades in an envelope or bag. You pick 2 cards at random and tell me “I have an Ace”. What is the probability that you have two aces?

Next suppose I pick 2 of the 6 cards at […]

## Mathematical Games Advent Calendar

*By toni On 28 November, 2016 · Leave a Comment*

This month we have a link to an Advent Calendar on the NRICH website which gives you a mathematical game when you click on any day in December up to Christmas Eve.

Some of the games you can play on the computer but for many of them do not need a […]

## Grades 9 to 12 Mathsland Lottery

*By toni On 11 August, 2016 · Leave a Comment*

In the Mathsland Lottery, 49 balls are numbered 1 to 49 and 6 balls are chosen at random without replacing any of the balls so that 6 different winning numbers are chosen.

Each lottery ticket has 6 numbers and you win a top prize if your 6 numbers match the 6 numbers chosen that […]

## Grades 5 to 12 In a Box

*By toni On 20 August, 2013 · 37 Comments*

Najwa and Zuki play a game.

They put two red and two blue ribbons in a box. They pull out two ribbons at the same time without looking at the colours.

Najwa wins if both ribbons are the same colour.

Zuki wins if the two ribbons are different colours.

Is this a fair […]

## Grades 9 to 12 Odds and Evens

*By toni On 29 January, 2013 · Leave a Comment*

In Game A you pick out two balls at random from a bag containing balls numbered 2, 3, 4, 5 and 6.. If the total is even you win. If it is odd you lose. Are you equally likely to win or to lose (a fair game)?

## Grades 7 to 10 Nines and Tens

*By toni On 19 March, 2012 · 24 Comments*

Both 9 and 10 can be made up in 2 different ways by adding pairs of the numbers 1, 2, … 6, that is

9 = 3 + 6 = 4 + 5

10 = 4 + 6 = 5 + 5

Explain why it is that when you throw two dice you are more […]

## Grade 9 to 12 – Two’s Company

*By toni On 19 March, 2012 · 2 Comments*

A container holds 4 yellow balls, 2 blue balls and a red ball. The balls are identical in all ways except colour. When you shake the container the balls settle into a hexagonal pattern as shown in the diagram.

You win if two blue balls touch.

How many different ways can […]

## Grades 4 to 7 Same Sweets

*By toni On 17 February, 2012 · 13 Comments*

A bag has a large number of green, white, orange, yellow and red sweets.

You pick sweets from the bag without looking. If you pick 2 sweets what different combinations of colours can you get?

## Grades 7 to 9 – One Step Two Steps

*By toni On 18 January, 2012 · Leave a Comment*

A staircase has 12 steps. You can go down the steps one at a time or two at time.

For example:

You could go down 1 step, then 1 step, then 2 steps, then 2, 2, 1, 1, 1, 1 as in the picture.

In how many different ways […]

## Grades 6 or 7 – Red Even

*By toni On 18 January, 2012 · Leave a Comment*

(a) You have a 3 by 3 grid and you must mark the squares to make 4 red squares and 5 blue squares.

How many ways can you do this so that all the rows columns and diagonals have an even number of red squares?

(b) Are there any additional solutions if […]

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