The GATE Grind

GATE 2017 ME (ME2) – Question 8

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

Four women P, Q, R, S and five men V, W, X, Y, Z must form four woman–man pairs. P cannot pair with Z, and Y must pair with someone. The number of ways is ______.

  1. 74
  2. 76
  3. 78
  4. 80

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 78

Explanation

Choose the other three men from the four besides Y in4ways and match the selected four men to the women in4!ways:96 arrangements. Forbidden arrangements fix P-Z, choose the other two men besides Y and Z in3ways, and pair the remaining women in3!ways:18. Valid count is96−18=**78, C**.