Which of the following is a way to write ?

If , then for all integers . What is the value of ?

29 travellers meet in a hostel. Among them, 21 speak French, 11 speak Spanish and 18 speak English. These counts include 9 travellers who speak Spanish and at least one of French and English. All the travellers speak at least one of the three languages and 1 of the travellers speaks all three. How many travellers speak French and English (including those who speak all three languages)?

The numbers 1 to 10 are arranged in a line (uniformly at random). What is the probability that the first number is odd and the last number is even?

[Reminder that for all quizzes in this unit you should enter probabilities as fractions (not decimals), and you must reduce them to their lowest terms. eg 3/4 but not 0.75 or 9/12.]

What is the coefficient of when is expanded?

32 travellers meet in a hostel. Among them, 20 speak French, 15 speak Spanish and 19 speak English. These counts include 12 travellers who speak Spanish and at least one of French and English. All the travellers speak at least one of the three languages and 3 of the travellers speak all three. How many travellers speak French and English (including those who speak all three languages)?

What is the coefficient of when is expanded?