The number of ways that 5 blue balls of different sizes and 5 red balls of different sizes can be arranged in a row so that no two balls of the same colour come together is

Consider 5 blue balls $\left(B_1,B_2,B_3,B_4,B_{\mathbf{5}}\right)$ as one unit. Consider 5 red balls $\left(R_1,R_2,R_3,R_4,R_{\mathbf{5}}\right)$as one unit.$\left(B_1,B_2,B_3,B_4,B_{\mathbf{5}}\right)$$\left(R_1,R_2,R_3,R_4,R_{\mathbf{5}}\right)$can be arranged in 2! ways  5 blue balls can be arranged in 5! ways and 5 red balls can be arranged in 5!ways

 No of ways $=2\times 5!\times 5!$