A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2017 · Q610 Marks
(a) Find the number of different 3-digit numbers greater than 300 that can be made from the digits 1, 2, 3, 4, 6, 8 if (b) A team of 5 is chosen from 6 boys and 4 girls. Find the number of ways the team can be chosen if
- (a)(i)no digit can be repeated,[3]
- (a)(ii)a digit can be repeated and the number made is even.[3]
- (b)(i)there are no restrictions,[1]
- (b)(ii)the team contains more boys than girls.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- EITHER: (M1 4P2 or 4C2x2! or 5 x 4 OE (considering final 2 digits)
- M1 Mult by 4 or summing 4 options (considering first digit)
- A1) Correct final answer
- OR: (M1 Calculating total number of values (with subtraction seen)
- M1 Calculating number of unwanted values
- A1) Correct final answer
- EITHER: (M1 6 linked to considering middle digit e.g. multiplied or in list
- M1 Multiply an integer by 4 x 4 (condone x 16)
- A1) (No additional figures present for both M's to be awarded)
- OR: (M1 Calculating total number of values (with subtraction seen)
- M1 Calculating number of unwanted values
- A1) Correct final answer
- B1 252
- M1 Multiplying 2 combinations nCq x mCr, q + r = 5, or 9C5 seen alone
- M1 Summing 2 or 3 appropriate outcomes, involving perm/comb, no extra outcomes.
- A1 Total = 186 ways
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →