Cambridge Additional Mathematics

258 Counting and the binomial expansion (Chapter 10)

The word and suggestsmultiplyingthe possibilities.

The word or suggestsaddingthe possibilities.

Example 2 Self Tutor

How many different paths

lead from P to Q?

EXERCISE 10B

1 How many different paths lead from P to Q?

ab

B Counting paths

A

D

B

P E G

C

F

Q

P

Q

A B C

D

E F

G H

I

P Q P Q

Consider the road system illustrated which shows

the roads from P to Q.

From A to Q there are 2 paths.

From B to Q there are 3 £2=6paths.

From C to Q there are 3 paths.

) from P to Q there are 2+6+3=11paths.

Notice that: ² When going from B to G, we go from B to Eand then from E to G. Wemultiply

the possibilities.

² When going from P to Q, we must first go from P to A or PtoBor PtoC.

Weaddthe possibilities from each of these first steps.

From P to A to B to C to Q there are 2 £3=6paths

or from P to D to E to F to Q there are 2 paths

or from P to D to G to H to I to Q there are 2 £2=4paths.

In total there are 6+2+4=12different paths.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_10\258CamAdd_10.cdr Friday, 4 April 2014 1:45:35 PM BRIAN