Let $A$ be the set $\{ 1,2 , \ldots , 6 \}$. How many functions from $A$ to $A$ are there such that the range of $f$ has exactly 5 elements? (a) 240 (b) 720 (c) 1800 (d) 10800
(D) Choose 2 domain elements mapping to 1 range element: ${}^6C_2 = 15$ ways. The 5 units map to 5 range elements: $5!$ ways. Choose 5 range elements from 6: ${}^6C_5 = 6$ ways. Total $= 15 \times 5! \times 6 = 10800$.
Let $A$ be the set $\{ 1,2 , \ldots , 6 \}$. How many functions from $A$ to $A$ are there such that the range of $f$ has exactly 5 elements?\\
(a) 240\\
(b) 720\\
(c) 1800\\
(d) 10800