A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2017 · Q59 Marks

A plate of cakes holds 12 different cakes. Find the number of ways these cakes can be shared between Alex and James if each receives an odd number of cakes.

(i)A plate of cakes holds 12 different cakes. Find the number of ways these cakes can be shared between Alex and James if each receives an odd number of cakes.[3]
(ii)Another plate holds 7 cup cakes, each with a different colour icing, and 4 brownies, each of a different size. Find the number of different ways these 11 cakes can be arranged in a row if no brownie is next to another brownie.[3]
(iii)A plate of biscuits holds 4 identical chocolate biscuits, 6 identical shortbread biscuits and 2 identical gingerbread biscuits. These biscuits are all placed in a row. Find how many different arrangements are possible if the chocolate biscuits are all kept together.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

[M1] Summing at least 4 ₁₂Cₓ combinations with x = odd numbers
[A1] Correct unsimplified answer (can be implied by final answer) (e.g. 12C1+12C3+12C5+12C7+12C9+12C11)
[A1] = 2048 Correct answer
[B1] 7! seen alone or multiplied only (cupcakes ordered)
[M1] multiplying by ₈P₄ o.e (placing brownies)
[A1] = 8467200 correct answer
[B1] 9! oe seen alone or as numerator
[M1] dividing by at least one of 6!,2! (removing repeated shortbread or gingerbread biscuits) ignore 4! if present
[A1] = 252 correct answer

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