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JAMB 1992 · UME · Q50

A student has 5 courses to take from Mathematics and Physics. There are 4 courses in Mathematics and 3 in Physics which he can choose from at will. In how many ways can he choose his courses so that he takes exactly two courses in Physics?

Worked solution (try it first)
  1. Exactly two Physics courses from 3: 3C2=3^3C_2 = 3 ways.
  2. The other 5−2=35 - 2 = 3 courses come from Mathematics, 3 from 4: 4C3=4^4C_3 = 4 ways.
  3. Each Physics choice goes with each Mathematics choice, so multiply: 3×4=123 \times 4 = 12, option B.

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