There are several tea cups in the kitchen, some with handle and the others without handles. The number of ways of selecting two cups without a handle and three with a handle is exactly 1200. What is the maximum possible number of cups in the kitchen?

Step-by-step solution

Let cups without handle equals to x & cups with handle equals to y aligned & ^x C₂ ^y C₃=1200=2^4 3 5^2 & x(x-1) 2 y(y-1)(y-2) 6 =2^4 3 5^2 & x=25, y=4 and x=16, y=5 & x+y is maximum when x=25, y=4 aligned maximum possible cups equals to 29