A-LevelMathematicsProbability and statistics9709/53 · May/June 2021 · Q610 Marks

The word REQUIREMENT has 11 letters.

(a)How many different arrangements are there of the 11 letters in the word REQUIREMENT?[2]
(b)How many different arrangements are there of the 11 letters in the word REQUIREMENT in which the two Rs are together and the three Es are together?[1]
(c)How many different arrangements are there of the 11 letters in the word REQUIREMENT in which there are exactly three letters between the two Rs?[3]
(d)Five of the 11 letters in the word REQUIREMENT are selected. How many possible selections contain at least two Es and at least one R?[4]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[2] M1 11! alone on numerator – must be a fraction. k! × m! on denominator, k = 1, 2, m = 1, 3, 1 can be implied but cannot both = 1. No additional terms
A1 Exact value only
[1] B1 Evaluate, exact value only
[3] M1 9!/3! ×k seen, k an integer > 0, no +, - or ÷
M1 7× an integer seen in final answer, no +, - or ÷
A1 Exact value only
[4] M1 Identifying four correct scenarios only.
B1 Correct number of selections unsimplified for 2 or more scenario.
M1 Adding the number of selections for 3 or 4 identified correct scenarios only, accept unsimplified. ³Cx x²Cy × ⁶Cz, x+y+z=5 correctly identifies x Es and y Rs
A1 WWW, only dependent upon 2nd M mark.

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