Question

Let a = f1; 2; 3; 4; 5; 6; 7; 8g. How many functions f : a ! A can be defined such that f(1) < f(2) < f(3)?

Answer 1

number of ways to select images for 1,2,3=

$\binom{8}{3} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$

remaining five elements can be assigned in 5! ways=120 ways

total number of required injective functions =56(120)

= 6720