Find the number of different arrangements that can be made of all 9 letters in the word CAMERAMAN in each of the following cases.
- (i)There are no restrictions.[2]
- (ii)The As occupy the 1st, 5th and 9th positions.[1]
- (iii)There is exactly one letter between the Ms.[4]
- (iv)Three letters are selected from the 9 letters of the word CAMERAMAN. Find the number of different selections if the three letters include exactly one M and exactly one A.[1]
- (v)Find the number of different selections if the three letters include at least one M.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] 9! alone on numerator, 2! and/or 3! on denominator
- [A1] Exact value, final answer
- [B1] Final answer
- [M1] 7! in numerator, (considering letters not M)
- [M1] Division by 3! only (removing repeated As)
- [M1] Multiply by 7 (positions of M-M)
- [A1] Exact value, final answer
- [M1] 6! in sum of 2 expressions a6! + b6!
- [M1] Multiply by 7 in both expressions (positions of M-M)
- [M1] (C/2! + D/3!) seen (removing repeated As)
- [A1] Exact value
- [M1] 7! in numerator (considering 6 letters + block)
- [M1] Division by 2! and 3! seen in different terms
- [M1] Summing 5 correct scenarios only
- [A1] Exact value
- [B1] Final answer
- [M1] Either option M M ^ or M ^ ^ correct, accept unsimplified
- [M1] Add 4 or 5 correct scenarios only
- [A1] Value must be clearly stated
- [M1] Either option M M^or M^^ correct, accept unsimplified
- [M1] Adding 2 or 3 correct scenarios only
- [A1] Value must be clearly stated
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