Chapter 2 Exercise 2 - Welcome -...
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Chapter 2 Exercise 2.1 Q. 1. {20, 21, 22, 23, 24, 25, 26, 27, 28, 29} Q. 2. Jelly (J) Fruit (Fr) Cake (C) Steak (S) SJ SFr SC Burger (B) BJ BFr BC Fish (F) FJ FFr FC Pasta (P) PJ PFr PC Q. 3. Coin H T Die 1 1H 1T 2 2H 2T 3 3H 3T 4 4H 4T 5 5H 5T 6 6H 6T Q. 4. Medium Large C CM CL H HM HL V VM VL 12 possible outcomes Q. 5. Outcomes ND NH NS NC PD PH PS PC D H S N P C D H S C Q. 6. (i) 20 (ii) 12 Q. 7. C C B C C C B A r 1 r 2 C 1
Transcript of Chapter 2 Exercise 2 - Welcome -...
Chapter 2 Exercise 2.1
Q. 1. {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
Q. 2. Jelly (J) Fruit (Fr) Cake (C)Steak (S) SJ SFr SC
Burger (B) BJ BFr BCFish (F) FJ FFr FC
Pasta (P) PJ PFr PC
Q. 3. CoinH T
Die
1 1H 1T2 2H 2T3 3H 3T4 4H 4T5 5H 5T6 6H 6T
Q. 4. Medium Large
C CM CLH HM HLV VM VL
12 possible outcomes
Q. 5. Outcomes
ND
NH
NS
NC
PD
PH
PS
PC
D
H
SN
P
C
D
H
S
C
Q. 6. (i) 20(ii) 12
Q. 7. C
CB
C
C
CB
A
r1
r2
C
1
2
Q. 8. Outcomes
RR
RY
RO
YR
YY
YO
OR
OY
OO
R
Y
O
R
Y
O
R
Y
O
R
Y
O
Q. 9. (i) 10 111 11 122 12 133 13 14
(ii) 3
Q. 10. T C W L CaT TT TC TW TL TCaC CT CC CW CL CCaW WT WC WW WL WCaL LT LC LW LL LCaCa CaT CaC CaW CaL CaCa
Q. 11. Outcomes3rd2nd1st
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG
BB
B
G
G
B
G
G
B
G
B
G
B
G
Q. 12. (i) 1 (ii) 5(iii) 18
3
Exercise 2.2
Q. 1. 5 × 4 = 20
Q. 2. 10 × 2 = 20
Q. 3. Five sizes Five colours Three styles
5 × 5 × 3 = 75
Q. 4. 5 × 2 = 10
Q. 5. 4 × 6 × 5 = 120
Q. 6. 10 × 3 × 5 = 150
Q. 7. 26 letters 10 digits
26 × 10 = 260
Q. 8. 4 × 3 = 12
Q. 9. 52 × 2 × 6 = 624
{Ace of Hearts, Head, two}
Q. 10. 65 = 7,776
Q. 11. 210 = 1,024
Q. 12. 4 Boys
3 Girls
4 × 3 = 12
Q. 13. Gold Silver Bronze
8 × 7 × 6 = 336
Q. 14. 26 × 25 × 24 × 23 = 358,800
Q. 15.
2 letters
3 digits
(i) 26 × 25 × 10 × 10 × 10 = 650,000 (ii) 26 × 26 × 10 × 9 × 8 = 486,720 (iii) 26 × 25 × 10 × 9 × 8 = 468,000
Exercise 2.3
Q. 1. (i) 24 + 120 ≠ 362,880 No
(ii) 6 × 24 = 479,001,600
144 ≠ 479,001,600 No
4
Q. 2. (i) 6 7 8
6 8 7
7 6 8
7 8 6
8 7 6
8 6 7
(ii) 4 (evens)
(iii) 2 (odd)
Q. 3. (i) list
(ii) 120 5 × 4 × 3 × 2 × 1 = 120 ways
Q. 4. (i) 3 × 2 × 1 = 6 ways (ii) 1 × 2 × 1 = 2.
T
(iii) 6 − 2 = 4.
Q. 5. (i) 5 × 4 × 3 × 2 × 1 = 120 ways
(ii) 1 × 4 × 3 × 2 × 1 = 24
(iii) 96 120 − 24 = 96
(iv) 4 × 3 × 2 × 1 × 1 = 24
M
Q. 6. (i) 6! = 720 ways
(ii) 1 5 4 3 2 1 = 120
(iii) Vowels = E, I, A
3 5 4 3 2 1 = 360
Q. 7. 6 × 5 × 4 = 120 ways
Q. 8. 9 10 10 10 = 9,000
0
Q. 9. 26 × 25 = 650 members
Q. 10. (i) 7! = 5,040 ways
(ii) 1 6 5 4 3 2 1 = 720
A
(iii) 1 5 4 3 2 1 1 = 120
A B
Q. 11. (i) 7! = 5,040
(ii) 1 × 6! = 720
(iii) 5,040 − 720 = 4,320
(iv) 3 × 6! = 2,160
(v) 5,040 − 2,160 = 2,880
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Q. 12. (i) 4 × 3 × 2 = 24
(ii) 4 × 4 × 4 = 64
(iii) ODD NO REPETITION
3 × 2 × 2 = 12
(iv) 24 − 12 = 12
Q. 13. (i) (a) 4 3 2 1 = 24
(b) 44 = 256
(ii) 3 3 2 1 = 18
1
cannot be 1
Q. 14. (i) 8! = 40,320
(ii) 1 × 7! = 5,040
(iii) 3 7 6 5 4 3 2 1 = 15,120
(iv) 3 2 1 5 4 3 2 1 = 720
Q. 15. (i) 9! = 362,880
(ii) 8 7 6 5 4 3 2 1 1 = 40,320
T
(iii) 5 × 8! = 201,600
(iv) 5! × 4! = 2,880
(v) 4! × 5! = 2,880
Q. 16. (i) 5! = 120 ways
(ii) 3 2 2 1 1 = 12 ways
G B G B G
Q. 17. (i) 11! = 39,916,800
(ii) 5! × 6! = 86,400
(iii) BGBG.…. 6! × 5! = 86,400
or +
GBGB.…. 5! × 6! = 86,400
Ans = 172,800 ways
Q. 18. (i) 6! = 720
(ii) 2 × 5! = 240 ways
(iii) 2 4 3 2 1 1 = 48 ways
Vowel T
(iv) 2 1 4 3 2 1 = 48 ways
V V
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(v) 5 4 3 2 1 = 120 ways OR 2 1 4 3 2 1
× 2 ways vowels × 5
240 ways = 240
(vi) 720 − 240 = 480 ways
Q. 19. (i) 7! = 5040
(ii) 2 × 1 × 5 × 4 × 3 × 2 × 1 = 240 ways
(iii) 6 5 4 3 2 1 × 2 ways AR can be arranged
Ans: 1,440 ways.
Exercise 2.4
Q. 1. (i) 10 (iii) 1365
(ii) 56 (iv) 435
Q. 2. (i) 184,756 (iii) 3,921,225
(ii) 2,118,760 (iv) 6
Q. 3. (i) 120 (iii) 1,001
(ii) 120 (iv) 12
Q. 4. (i) 120 (iii) 19
(ii) 1 (iv) 1
Q. 5. (i) 1 + 11 = 12
(ii) 84 × 210 = 17,640
(iii) 1,001 ÷ 364 = 2.75
(iv) 5(6) + 2(15) × 2(20) = 1,230
Q. 6. (i) 10 + 10 = 20
20 = 20
(ii) 84 − 56 = 28
28 = 28
(iii) 2,002 + 3,003 = 5,005
5,005 = 5,005
(iv) 11 + 55 = 66
66 = 66
Q. 7. 10 + 10 ≠ 252
20 ≠ 252
No
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Q. 8. (i) ( 12 x ) = ( 12 4 ) Verification ( 12 8 ) = ( 12 4 ) 495 = 495
x = 8
(ii) x = 5 ( 19 5 ) = ( 19 14 ) 11,628 = 11,628
(iii) x = 12 ( 22 10 ) = ( 22 12 ) 646,646 = 646,646
Q. 9. (i) ( n 2 ) = 28 ⇒ n(n – 1)
_______ 2 × 1 = 28 ⇒ n2 – n =56
n2 – n – 56 = 0
(n + 7)(n – 8) = 0
n = –7 or n = 8
Check: 8C2 = 28
(ii) ( n 2 ) = 15 ⇒ n2 – n ______ 2 = 15 ⇒ n2 – n =30
n2 – n – 30 = 0
(n – 6)(n + 5) = 0
n = 6 or n = –5
Check: 6C2 = 15
Exercise 2.5
Q. 1. ( 22 15 ) = 170,544
Q. 2. ( 20 2 ) = 190
Q. 3. ( 15 3 ) = 455
Q. 4. 14C4 = 1,001
Q. 5. 45C6 = 8,145,060
Q. 6. (i) ( 30 15 ) = 155,117,520
(ii) ( 25 10 ) = 3,268,760
Q. 7. ( 13 2 ) = 78
Q. 8. (i) ( 50 8 ) = 536,878,650
(ii) ( 46 4 ) = 163,185
(iii) ( 49 8 ) = 450,978,066
or
536,878,650 – song must be on it ( 49 7 ) = 536,878,650 − 85,900,584
= 450,978,066
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Q. 9. ( 42 3 ) = 11480
Q. 10. (i) ( 9 4 ) = 126 (ii) ( 7 2 ) = 21 (iii) ( 8 4 ) = 70
Q. 11. (i) ( 10 2 ) = 45 (ii) ( 9 1 ) = 9 (iii) ( 5 2 ) = 10
Q. 12. ( 17 2 ) = 136
Q. 13. (i) ( 7 3 ) = 35 (iii) ( 6 3 ) = 20
or
35 − 15 = 20
(ii) ( 6 2 ) = 15 (iv) ( 5 1 ) = 5
Q. 14. (i) ( 10 2 ) = 45
(ii) ( 10 3 ) = 120
Q. 15. ( 22 2 ) × 2 = 412 games
Q. 16. ( 20 4 ) ( 7 5 ) = (4845) × (21) = 101,745
Q. 17. ( 10 3 ) ( 15 2 ) = (120)(105)
= 12,600
Q. 18. ( 20 5 ) ( 5 2 ) = (15504)(10)
= 155040
Q. 19. ( 3 2 ) × ( 3 1 ) × ( 3 2 ) = 3 × 3 × 3
= 27
Q. 20. (i) ( 12 3 ) = 220
(ii) ( 5 3 ) ( 7 0 ) = (10)(1)
= 10
(iii) ( 7 2 ) ( 5 1 ) = 21 × 5 = 105
or
( 7 3 ) ( 5 0 ) = 35 × 1 = 35
Ans 105 + 35 = 140
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Q. 21. (i) ( 16 3 ) = 560
(ii) ( 10 2 ) ( 6 1 ) = 270
(iii) 2 Women 1 Man = 270
or
3 Women No Men
( 10 3 ) ( 6 0 ) = 120
270 + 120 = 390
Q. 22. (i) ( 25 5 ) = 53,130
(ii) ( 10 3 ) ( 15 2 ) = 12,600
(iii) ( 10 2 ) ( 15 3 ) = 20,475
or
( 10 3 ) ( 15 2 ) = 12,600
20,475 + 12,600 = 33,075
(iv) ( 9 3 ) ( 14 0 ) or ( 9 2 ) ( 14 1 ) or ( 9 1 ) ( 14 2 ) or ( 9 0 ) ( 14 3 ) = 84 + 504 + 819 + 364
= 1,771
Revision Exercises
Q. 1. (i) L M SP PL PM PS
LCD LCDL LCDM LCDS
(ii) 6
Q. 2. OutcomesSizeSleeve Colour
SBM
SBL
SBLM
SBLL
SWM
SWL
LOBM
LOBL
LOBLM
LOBLL
LOWM
LOWL
M
LBlack
Blue
White
S
L
Black
Blue
White
M
L
M
L
M
L
M
L
M
L
Q. 3. 4 × 7 = 28
10
Q. 4. (i) C
B
C
A
A
B
C
B
C
A
A
B
C
A
B
(ii) List {ABC, .… }
(iv) 2
(v) 1
Q. 5. (i) ( 10 6 ) = 210
(ii) ( 9 5 ) = 126
Q. 6. (i) 6! = 720
(ii) 2 × 5 × 4 × 3 × 2 × 1 = 240
(iii) 2 4 3 2 1 1 = 48
Q. 7. (i) ( 12 2 ) = 66
(ii) ( 5 1 ) ( 7 1 ) = 35
(iii) ( 5 2 ) ( 7 0 ) = 10
(iv) ( 5 1 ) ( 7 1 ) = 35 remember at least one girl means 1 or more
or
( 5 2 ) ( 7 0 ) = 10
Ans: 45
Q. 8. (i) 5! = 120 ways
(ii) 1 × 4 × 3 × 2 × 1 = 24
(iii) 2 × 4 × 3 × 2 × 1 = 48
(iv) 3 × 4 × 3 × 2 × 1 = 72
Q. 9. (i) 6 5 4 3 2 1 = 720
(ii) 2 5 4 3 2 1 = 240
(iii) 2 1 4 3 2 1 = 48
(iv) 4 3 2 1 2 1 = 48
(v) 5 4 3 2 1 × 2 = 240
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Q. 10. (i) ( 10 4 ) = 120
(ii) ( 9 3 ) = 84
(iii) 210 − 84 = 126
Q. 11. (i) 5! = 120
(ii) 3 4 3 2 1 = 72
(iii) 3 3 2 1 2 = 36
(iv) 3 2 1 2 1 = 12
(v) 4 3 2 1 × 2 = 48
Q. 12. (i) 4 3 2 1 = 24
(ii) 1 3 2 1 = 6
(iii) 3 2 1 2 = 12
(iv) 3 2 1 1 = 6
(v) 1 2 1 1 = 2
Q. 13. (i) ( 10 4 ) = 210
(ii) ( 9 3 ) = 84
(iii) ( 7 1 ) ( 3 3 ) = 7
(iv) 3 or 4 girls
( 7 3 ) ( 3 1 ) = 105
( 7 4 ) ( 3 0 ) = 35
105 + 35 = 140
Q. 14. (i) 8 7 6 5 4 3 2 1 = 40,320
(ii) 1 × 7! = 5,040
R
(iii) 3 7 6 5 4 3 2 1 = 15,120
(iv) 3 2 1 5 4 3 2 1 = 720
(v) 6 5 4 3 2 1 × 6 = 4,320
The three vowels can be arranged in six ways.
Q. 15. (i) 9! = 362,880
(ii) 5! × 4! = 2,880
(iii) 5 4 4 3 3 2 2 1 1 = 288
12
Q. 16. (i) 5! = 120
(ii) 1 4 3 2 1 = 24
(iii) 4 3 2 1 3 = 72
(iv) 1 3 2 1 3 = 18
Q. 17. (i) ( 52 4 ) = 270,725
(ii) ( 13 4 ) = 715
(iii) ( 4 4 ) = 1
(iv) ( 4 2 ) ( 4 2 ) = 36
(v) ( 4 2 ) ( 48 2 ) = 6,768
or
( 4 3 ) ( 48 1 ) = 192
( 4 4 ) ( 48 0 ) = 1
6,768 + 192 + 1 = 6,961
Q. 18. (i) ( 11 0 ) = ( 11 n ) n = 11
(ii) ( n 5 ) = ( n 6 ) n = 11
n − 5 = 6 n = 11
(iii) ( n 2 ) = 21 n(n – 1)
_______ 2 = 21
n2 − n = 42
(n + 6)(n − 7)
n − 1
