(a) E = {x: x is an integer 10 ≤ x ≤ 40} P = {x : x is a multiple of 6} Q = {x: x is a square number}

1. (a)(i)Write down the elements of P U Q.[1]
2. (a)(ii)Find n(P' ∩ Q).[1]
3. (b)Use set notation to describe the shaded region in the Venn diagram. [Figure of Venn Diagram with E, B, C, D][1]
4. (c)(i)In a college, students can study French (F), Spanish (S) and Arabic (A). A group of 25 students are asked which languages they study. Some of the results are shown in the Venn diagram. [Figure of Venn Diagram with F, S, A and numbers 5, 1, 4, 2] All students who study both Arabic and Spanish also study French. 7 students study French only. 8 students study Arabic. Use this information to complete the Venn diagram.[2]
5. (c)(ii)Two of the 25 students are selected at random. Find the probability that they both study Spanish only.[2]
6. (c)(iii)Three of the students are selected at random from those who study French. Find the probability that only one of them also studies Arabic.[3]

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