In a bag there are 5 red, 3 white and 4 black balls. Four balls are drawn from the bag. The number of ways in which at most 3 reel balls are selected is

At most 3 red balls can be drawn in the following
ways

$\begin{array}{ccc}\text{ Number of red balls }& \text{ Other colour balls }& \text{ Number of ways }\\ 0& 4& { }^7{C}_4\\ 1& 3& { }^5{C}_1{\times }^7{C}_3\\ 2& 2& { }^5{C}_2{\times }^7{C}_2\\ 3& 1& { }^5{C}_3{\times }^7{C}_1\end{array}$

Hence, required number of ways

$\begin{array}{l}{=}^7{C}_4{+}^5{C}_1{\times }^7{C}_3{+}^5{C}_2{\times }^7{C}_2{+}^5{C}_3{\times }^7{C}_1\\ =35+175+210+70=490\end{array}$