Using binomial coefficients, the new simple and efficient algorithms for the accurate and fast calculation of the Clebsch-Gordan and Gaunt coefficients, and Wigner n - j symbols for n = 3, 6, 9 are presented. For quick calculations, the binomial coefficients are stored in the memory of the computer. It is demonstrated that the use of binomial coefficients greatly reduces the CPU time. The numerical results presented are in complete agreement with those obtained in the alternative evaluation procedure. The method suggested is completely general and free of any restrictions.