A group of 8 scientist is composed of 5 chemist and 3 biologist. In how many ways can a committe of 5 be formed that has 3 chemist and 2 biologist? Using mathematical induction prove that 1³ + 2³ + 3³ + ……………….. + n³ = n²(n + 1)² / 4) for n ≥ 1.