260 Counting and the binomial expansion (Chapter 10)EXERCISE 10C.1
1 Findn!for n=0, 1 , 2 , 3 , ...., 10.2 Simplify without using a calculator:a 6!
5!b 6!
4!c 6!
7!d 4!
6!e 100!
99!f 7!
5!£2!3 Simplify:a
n!
(n¡1)!b
(n+ 2)!
n!c
(n+ 1)!
(n¡1)!Example 4 Self Tutor
Express in factorial form:
a 10 £ 9 £ 8 £ 7 b
10 £ 9 £ 8 £ 7
4 £ 3 £ 2 £ 1a 10 £ 9 £ 8 £7=
10 £ 9 £ 8 £ 7 £ 6 £ 5 £ 4 £ 3 £ 2 £ 1
6 £ 5 £ 4 £ 3 £ 2 £ 1=
10!
6!b
10 £ 9 £ 8 £ 7
4 £ 3 £ 2 £ 1
=
10 £ 9 £ 8 £ 7 £ 6 £ 5 £ 4 £ 3 £ 2 £ 1
4 £ 3 £ 2 £ 1 £ 6 £ 5 £ 4 £ 3 £ 2 £ 1
=
10!
4!£6!4 Express in factorial form:
a 7 £ 6 £ 5 b 10 £ 9 c 11 £ 10 £ 9 £ 8 £ 7d
13 £ 12 £ 11
3 £ 2 £ 1e
1
6 £ 5 £ 4f
4 £ 3 £ 2 £ 1
20 £ 19 £ 18 £ 17Example 5 Self Tutor
Write as a product by factorising:
a 8! + 6! b 10!¡9! + 8!a 8! + 6!
=8£ 7 £6! + 6!
= 6!(8£7+1)
=6!£ 57b 10!¡9! + 8!
=10£ 9 £8!¡ 9 £8! + 8!
= 8!(90¡9+1)
=8!£ 82If your problem involves factorials of large numbers then it is important to cancel as many factors as possible
before using a calculator to evaluate the rest.For example, if you have
300!
297!
in your problem, you will find you cannot calculate300!on your calculator.
However, we can see that
300!
297!=
300 £ 299 £ 298 £297!
297!= 300£ 299 £ 298
= 26 730 600.cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_10\260CamAdd_10.cdr Monday, 6 January 2014 9:44:33 AM BRIAN