ANSWER A AND B WITH SOLUTIONS:

A. Find the value of n and r of the following:

1. If C (n, r) = 1 and P (n, r) = 120
2. If C (n, r) = 20 and P (n, r) = 120
3. If C (n, r) = 28 and P (n, r) = 56
4. If C (n, r) = 3 and P (n, r) = 6
5. If C (n, r) = 21 and P (n, r) = 42

B. Following are set of permutation and combination problems. Answer them and show your solutions.

1. In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?
2. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
3. There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?