7. A woman has nine close friends. (a) In how many ways can she invite six of th

Question

7. A woman has nine close friends.

                  (a) In how many ways can she invite six of these to dinner?

                  (b) Repeat (a) if two of her friends are divorced (from each other) and will not attend together.

                  (c) Repeat (a) if the friends consist of three single people and three married couples and, if a husband or wife is invited the spouse must be invited too.

8. A diagonal of a polygon is a line joining two nonadjacent vertices.

                  (a) How many diagonals does an octagon have?

                  (b) Loonie is the colloquial name for a Canadian one dollar coin. It has the shape of a regular 11-sided polygon. How many diagonals does a loonie have?

9.              (a) How many diagonals does a regular n-sided polygon have?

                  (b) Which regular n-sided polygon has three times as many diagonals as sides?

Explanation / Answer

7. (i) 9C2 (ii) 7C6 + 8C6 (iii) 9C3 + (9C2*5C2)  

8. (i) 8C2 (ii) 11C2

9. (i) nC2  (ii) 5

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