A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2024 · Q79 Marks

The word INTELLECT has 9 letters.

(a)How many different arrangements are there of the 9 letters in the word INTELLECT in which the two Ts are together?[2]
(b)How many different arrangements are there of the 9 letters in the word INTELLECT in which there is a T at each end and the two Es are not next to each other?[3]
(c)Four letters are selected at random from the 9 letters in the word INTELLECT. Find the percentage of the possible selections which contain at least one E and exactly one T.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[M1] k! / 2!m! k = 7 or 8, m = 1, 2.
[A1]
[M1] 7! / 2!2! – r, r integer >1.
[M1] 6! / 2! – t, s integer > 360.
[A1]
[B1] Either identified or correct unsimplified expression, either alone or in an addition. (for TE__ = 2C1 x 2C1 x 5C2 = 40)
[B1] Either identified or correct unsimplified expression, either alone or in an addition. (for TEE_ = 2C1 x 2C2 x 5C1 = 10)
[M1] a / ⁹C₄, a an integer < 126. Denominator value must be seen as ⁹C₄ somewhere.
[A1] 39.68 ≤ percentage ≤ 39.7.

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