1 Evaluate (a) P(8, 6) (b) P(11, 7) () 12 (d) 12 (c) (e)

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Chapter1: Combinatorial Analysis
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EXERCISES 29.9
Expand
(a) (a+ b) (b) (1+x)6 (c) (p+q)$
Evaluate
(a) P(8, 6)
(b) P(11, 7)
(1)
(4)
Primary and secondary routes connecting two
computers need to be chosen. Two primary routes are
needed from eight which are suitable and three
secondary routes must be chosen from four available.
In how many ways can the routes be chosen?
(c)
(d)
(e)
Write out explicitly
(3)
(a)
(b)
(c)
A combination lock can be opened by dialling three
correct letters followed by three correct digits. How
many different possibilities are there for arranging the
letters and digits? Is this more secure than a lock
which has seven digits? Is the word 'combination'
being used correctly?
3 The expansion of (a+b)" where n is a positive integer
may be written with the help of combination notation.
(a + b)" = d" +
(") a"-22 +..
A nuclear power station is to be built on one of 20
possible sites. A team of engineers is commissioned to
n-
examine the sites and rank the three most favourable
in order. In how many ways can this be done?
d"-kk
k=0
Solutions
1 (a) 20 160
(b) 1 663 200
(c) 220
(c) p +5p*q+ 10p'q² + 10p q +5pq +q°
(d) 455
(e) 455
4 112
2 (а) 1
(b) п
n(n - 1)
(c)
17576 000. Yes, it is more secure. Combination is not
3 (a) at + 4a b+6a?b² +4ab³ +64
being used correctly: permutation lock would be
better.
(b) 1+ 6x + 15x² + 20x + 15x + 6x + x
6840
Transcribed Image Text:EXERCISES 29.9 Expand (a) (a+ b) (b) (1+x)6 (c) (p+q)$ Evaluate (a) P(8, 6) (b) P(11, 7) (1) (4) Primary and secondary routes connecting two computers need to be chosen. Two primary routes are needed from eight which are suitable and three secondary routes must be chosen from four available. In how many ways can the routes be chosen? (c) (d) (e) Write out explicitly (3) (a) (b) (c) A combination lock can be opened by dialling three correct letters followed by three correct digits. How many different possibilities are there for arranging the letters and digits? Is this more secure than a lock which has seven digits? Is the word 'combination' being used correctly? 3 The expansion of (a+b)" where n is a positive integer may be written with the help of combination notation. (a + b)" = d" + (") a"-22 +.. A nuclear power station is to be built on one of 20 possible sites. A team of engineers is commissioned to n- examine the sites and rank the three most favourable in order. In how many ways can this be done? d"-kk k=0 Solutions 1 (a) 20 160 (b) 1 663 200 (c) 220 (c) p +5p*q+ 10p'q² + 10p q +5pq +q° (d) 455 (e) 455 4 112 2 (а) 1 (b) п n(n - 1) (c) 17576 000. Yes, it is more secure. Combination is not 3 (a) at + 4a b+6a?b² +4ab³ +64 being used correctly: permutation lock would be better. (b) 1+ 6x + 15x² + 20x + 15x + 6x + x 6840
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