Discussion questions · Section 2 of 3

Naval signals are made by arranging coloured flags in a vertical line and the flags are read from top to bottom. How many different signals can be made from 1 green, 3 red and 2 blue flags if

(i) all 6 of the flags are used,

(ii) at least 5 of them are used?

Three single men, two single women and two families take their places at a round table. Each of the two families consists of two parents and one child. Find the number of possible seating arrangements if

(i) members of the same family are seated together and the two single women are separated,

(ii) the seats are numbered and each child sits between their parents.

A box contains 8 balls, of which 3 are identical (and so are indistinguishable from one another) and the other 5 are different from each other. 3 balls are to be picked out of the box, the order in which they are picked out does not matter. Find the number of different possible selections of 3 balls.

Using the letters of the word CORRELATION, find the number of

(i) arrangements such that the two letters A and T are next to each other,

(ii) 6-letter code words that can be formed.

The salad bar at a restaurant has 6 separate bowls containing lettuce, tomatoes, cucumber, radishes, spring onions and beetroot respectively. John decides to visit the salad bar and make a selection. At each bowl, he can choose to take some of the contents or not.

(i) Assuming that John takes some of the contents from at least one bowl, find how many different selections he can make.

(ii) John decides he is going to have 4 salad items, and one of them will be tomatoes. How many different selections can he make?

A group of 10 people consists of 3 married couples and 4 single men.

(a) A committee of 4 is to be formed from the 10 people.

(i) How many different committees can be formed?

(ii) How many different committees can be formed if the committee can consist of at most 1 married couple?

(iii) How many different committees can be formed if the committee consists of at least one man and at least one woman?

(b) The group sits at a round table with 10 seats.

(i) If each man sits next to his wife, how many ways can they be seated?

(ii) If one particular man is absent and the rest are allowed to sit without any restrictions, how many ways can they be seated?

(iii) If a particular couple is absent and the rest are allowed to sit without any restrictions, how many ways can they be seated?