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CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2 · Question 5(a)(ii)

Ten students applied for mathematics scholarships: three females and seven males. Four scholarships are awarded.

Determine the number of possible ways in which a group of FOUR applicants may be selected if at least one of the successful applicants must be female.

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Other parts of this question

  1. 5(a)(i)Determine the number of possible ways in which a group of FOUR applicants may be selected if no restrictions are applied.[1 mark]
  2. 5(b)(i)Determine the greatest possible amount of numbers that may be formed.[4 marks]
  3. 5(b)(ii)Determine the probability that a number formed is greater than 100.[3 marks]
  4. 5(c)(i)Rewrite the system of equations as an augmented matrix.[2 marks]
  5. 5(c)(ii)Use elementary row operations to reduce the system to echelon form.[5 marks]
  6. 5(c)(iii)Hence, solve the system of equations.[3 marks]
  7. 5(c)(iv)Show that the system has no solution if the third equation is changed to 1.5x - 1.5y + 3z = 9.[4 marks]

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