The number of strictly increasing functions f from the set 1,2,3,4,5,6 to the set 1,2,3, ., 9 such that f(i) i for 1 i 6 , is equal to :

Step-by-step solution

For strictly increasing f , if we choose elements a₁ Since f(i) i always, condition f(i) i means f(i) i + 1 for all i . Let h(i) = f(i) - i . Then h(i) 1 , h(6) 3 , and h is non-decreasing. So h(i) 1, 2, 3 for all i . Number of non-decreasing sequences of length 6 from 1, 2, 3 = 8 2 = 28 .