Review practice · Section 3 of 3

A committee of eight people is chosen from 9 men and 10 women. Find the number of ways it can be chosen with at least 3 men and 3 women.2 marks

In the end four couples—Mr/Mrs Akira, Mr/Mrs Balthus, Mr/Mrs Chan and Mr/Mrs Ravi—form the committee and sit around a table for a meal.

(i) Find the number of arrangements if all the women sit together.2 marks

(ii) Find the number of arrangements if Mr Akira, Mr Chan and Mr Ravi refuse to sit next to each other.2 marks

(iii) Each diner may order at most one dessert from chocolate fudge pie, lemon cake, tiramisu martini and baked Alaska. Find the number of possible selections for the table, given that at least one diner orders a dessert and the sequence of ordering is not important.2 marks

Three families comprising six adults and three children go on an outing to a theme park and travel together for the day.

(i) There are 15 amusement rides. A child insists on trying at least 2 of them. Calculate the number of ways this can be done.2 marks

(ii) On the Mummy Surprise rollercoaster, a passenger car has seats in 3 rows and 3 columns as shown.

(a) Calculate the number of ways the families can be seated without restrictions.1 mark

(b) Tom, the youngest child, insists on sitting next to his mother. Calculate the number of ways this can be done.2 marks

(iii) At lunch they are allocated a circular table with 9 seats. Calculate the seating arrangements if none of the children sit together.2 marks

Mr and Mrs Tan have a son David and invite 6 guests for dinner. Before dinner, all 9 diners stand in a straight row for a group photo. Find the arrangements if

(i) all 9 diners may stand anywhere,1 mark

(ii) the Tan family members must be separated.2 marks

The diners then sit at two round tables, a five-seater and a smaller four-seater. Find the arrangements if

(iii) anyone may sit at either table,2 marks

(iv) David must sit between his parents at either table.3 marks

Four married couples attend a wedding dinner. One couple brings two children. Find the ways these ten people can sit around a table if

(i) there are no restrictions,1 mark

(ii) each couple must sit together.3 marks

They take a photo with the bride and bridegroom. The twelve people arrange themselves in two rows of six, with the bride and bridegroom together in the middle of the front row. How many arrangements also place both children in the front row?3 marks