Application of FCP to Counting Problems (Grade 12 NSC Matric Mathematics): Flashcards

Multiply the number of available options at each step

Treat them as a single unit

Total valid = All possible - Forbidden arrangements

$\frac{n!}{n_1! \times n_2! \times ... \times n_k!}$

$8 \times 7 \times 6 = 336$ ways

$6! \times 2! = 1440$ ways

$\frac{3!}{2!} = 3$ arrangements

$\frac{7!}{2! \times 2!} = 1260$ arrangements

$6 \times 5 \times 4 = 120$ numbers

Use complementary counting: all - unwanted