please show all your work neatly on paper

1. A committee of 5 shareholders is to be chosen from a larger group of 7 men and 5 women. How many committees can be formed that consist of two men and three women? (2 marks: 1 mark for correct combinations, 1 mark for choosing combining combinations) 2. Solve for n in the equation: 3(, C4 ) = 5(n-Cs) (4 marks: 2 marks for reducing factorial expressions, 1 mark for solving equations involving combinations, 1 mark for expressing your answer correctly) 3. Find the value of 'n' that satisfies the equation: ,C4 =, C, (1 mark for the correct value of n) 4. Explain, with an example, the difference between a permutation and a combination. (2 marks: 1 mark for example, 1 mark for difference) 5. Why must n 2 r in the notation ,C, ? (1 mark for explanation)