A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2025 · Q710 Marks
How many different arrangements are there of the 10 letters in the word SEYCHELLES?
- (a)How many different arrangements are there of the 10 letters in the word SEYCHELLES?[1]
- (b)How many different arrangements are there of the 10 letters in the word SEYCHELLES in which there are exactly two letters between the Ss and one of these two letters is C?[3]
- (c)How many different arrangements are there of the 10 letters in the word SEYCHELLES in which there is an S at the beginning, an S at the end and the three Es are not all next to each other?[3]
- (d)5 letters are selected at random from the 10 letters in the word SEYCHELLES. Find the probability that these 5 letters include the three Es.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [B1] CAO.
- [M1] 7!/(2!3!) × k, 1≤k, a positive integer.
- [M1] Integer ×7.
- [A1]
- [M1] 6!/(2!3!)xl, 6!/(2!2!)xm and 6!/(3!)xn seen. 1<l,m,n, positive integers.
- [M1] Summing 4 correct or correctly identified scenarios, oe.
- [A1]
- [M1] 8!/(2!3!) - q, 1<q<3360.
- [M1] m - 6!/(2!), m>360.
- [A1] 3000
- [B1] 7C2 (= 21) seen with no addition, subtraction, multiplication.
- [M1] Seen. (Total number of ways is 10C5 = 252).
- [A1] If M mark not awarded, SCB1 for 21/252, 1/12 www.
- [B1] 3/11 x 2/6 x 3/11.
- [M1] 5C2 x k, 0<k<1. Accept 5C3 x k, 0<k<1.
- [A1] If M mark not awarded, SCB1 for 21/252, 1/12 www.
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