Cambridge Additional Mathematics

266 Counting and the binomial expansion (Chapter 10)

13 3 boys and 3 girls are to sit in a row. How many ways can this be done if:

a there are no restrictions b there is a girl at each end

c boys and girls must alternate d all the boys sit together?

14 How many three-digit numbers can be made using the digits 0 , 1 , 3 , 5 , and 8 at most once each, if:

a there are no restrictions b the numbers must be less than 500

c the numbers must be even and greater than 300?

15

chosen if:

a there are no restrictions b at least one vowel (A or O) must be used

c the two vowels are not together?

16 Alice has booked ten adjacent front-row seats for a basketball

game for herself and nine friends.

a How many different arrangements are possible if there

are no restrictions?

b Due to a severe snowstorm, only five of Alice’s friends

are able to join her for the game. In how many different

ways can they be seated in the 10 seats if:

i there are no restrictions

ii any two of Alice’s friends are to sit next to her?

Discovery 1 Permutations in a circle

There are 6 permutations on the symbols A, B, and Cin a line. These are:

ABC ACB BAC BCA CAB CBA.

Howeverin a circlethere are only 2 different permutations on these 3 symbols. They are the only

possibilities with different right-hand and left-hand neighbours.

In contrast, these three diagrams show the same cyclic permutation:

What to do:

1 Draw diagrams showing different cyclic permutations for:

a one symbol: A b two symbols: A and B

c three symbols: A, B, and C d four symbols: A, B, C, and D

A

B

C

A

C

B

A

B

C

C

A

B

B

C

A

Consider the letters of the word MONDAY. How many permutations of four different letters can be

Permutations in a circle are

not required for the syllabus.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_10\266CamAdd_10.cdr Friday, 4 April 2014 1:50:02 PM BRIAN