Problem
COM-B1-M03-P020 At Least Three Red
#20
★★★☆☆ Level 3 of 5
There are \(10\) red and \(8\) blue balls. In how many ways can \(5\) balls be chosen with at least \(3\) red balls?
Split into \(3,4,5\) red balls.
Cases: \(3\) red and \(2\) blue: \(\binom{10}{3}\binom{8}{2}=3360\); \(4\) red and \(1\) blue: \(\binom{10}{4}\binom{8}{1}=1680\); \(5\) red: \(\binom{10}{5}=252\). Total: \(5292\).
Practice with “at least”.