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

5

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

6

(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

7

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

8

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

9

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

11

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