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CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 5(c)(i)

A committee consisting of 3 men and 2 women is to be formed from a group of 6 men and 4 women. However, it is known in advance that 2 of the men who dislike each other will not serve together on the committee.

In how many different ways can the committee be formed?

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Other parts of this question

  1. 5(a)Given that the matrix A = [[1-p, 3, -2], [2, p, -1], [-3, 2, 1]] is singular, calculate the value(s) of p.[6 marks]
  2. 5(b)Use row reduction to solve the following system of equations: 3x - 4y + z = 16; 2x + y - 2z = 5; x + 2y - z = -2.[9 marks]
  3. 5(c)(ii)What is the probability that the committee formed will contain neither of the 2 men who refuse to serve together?[3 marks]

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