Question and Answers Forum

Permutation and CombinationQuestion and Answers: Page 11

Question Number 125191 Answers: 0 Comments: 4

In how many ways can 3 men and 5 women be seated in a row if 3 specific women cannot sit next to each other? My solution: arrangements when the 3 women cannot sit next to eachother = 5! ×^6 P_3 = 14,400 Solution in book: arrangements with no restrictions = 8! arrangements with the 3 women seated next to eachother = 3! × 6! arrangements when the 3 women cannot sit next to eachother = 8! − (3! × 6!) = 36,000 I′m confused. Can I please get some explanation why my solution is wrong?

$In how many ways can 3 men and 5$ $women be seated in a row if 3 specific$ $women c a n n o t sit next to each other ?$ $My solution :$ $arrangements when the 3 women$ $c a n n o t sit next to eachother$ $= 5! \times^{6} P_{3}$ $= 14, 400$ $Solution in book :$ $arrangements with no restrictions = 8!$ $arrangements with the 3 women$ $seated next to eachother = 3! \times 6!$ $arrangements when the 3 women$ $c a n n o t sit next to eachother$ $= 8! - (3! \times 6!)$ $= 36, 000$ $I^{'} m confused . Can I please get some$ $explanation why my solution is wrong ?$

Question Number 124916 Answers: 2 Comments: 0

The number of ways arrangements of the word ′MASKARA′ with exactly 2 A′s are adjacent??

$T h e n u m b e r o f w a y s a r r a n g e m e n t s$ $o f t h e w o r d^{'} {M A S K A R A}^{'} w i t h e x a c t l y$ $2 A^{'} s a r e a d j a c e n t ? ?$

Question Number 124878 Answers: 3 Comments: 0

20 students should stand in 5 different rows. each row should have at least 2 students. in how many ways can you arrange them?

$20 s t u d e n t s s h o u l d s t a n d i n 5$ $d i f f e r e n t r o w s . e a c h r o w s h o u l d h a v e$ $a t l e a s t 2 s t u d e n t s . i n h o w m a n y w a y s$ $c a n y o u a r r a n g e t h e m ?$

Question Number 124829 Answers: 2 Comments: 0

How many ways are there to arrange the letters of the word ′ALAMATAR′ if no two A′s are adjacent?

$H o w m a n y w a y s a r e t h e r e t o a r r a n g e$ $t h e l e t t e r s o f t h e w o r d^{'} {A L A M A T A R}^{'} i f$ $n o t w o A^{'} s a r e a d j a c e n t ?$

Question Number 124826 Answers: 2 Comments: 0

How many ways are there to arrange the letters of the word ′ VISITING′ if no two I′s are adjacent ?

$H o w m a n y w a y s a r e t h e r e t o a r r a n g e$ $t h e l e t t e r s o f t h e w o r d^{'} {V I S I T I N G}^{'}$ $i f n o t w o I^{'} s a r e a d j a c e n t ?$

Question Number 124806 Answers: 2 Comments: 0

Question Number 124712 Answers: 2 Comments: 0

In how many ways can 5 boys and 3 girls be seated around a table if (i) boy B_3 and G_2 are not adjacent (ii) no girls are adjacent

$I n h o w m a n y w a y s c a n 5 b o y s a n d 3 g i r l s$ $b e s e a t e d a r o u n d a t a b l e i f$ $(i) b o y B_{3} a n d G_{2} a r e n o t a d j a c e n t$ $(i i) n o g i r l s a r e a d j a c e n t$

Question Number 124709 Answers: 2 Comments: 0

Between 20000 and 70000 find the number of even integers in which no digits is repeated

$B e t w e e n 20000 a n d 70000$ $f i n d t h e n u m b e r o f e v e n i n t e g e r s$ $i n w h i c h n o d i g i t s i s r e p e a t e d$

Question Number 124678 Answers: 0 Comments: 0

Question Number 124400 Answers: 2 Comments: 0

How many six-digit numbers contain exactly three different digits?

$H o w m a n y s i x - d i g i t n u m b e r s c o n t a i n$ $e x a c t l y t h r e e d i f f e r e n t d i g i t s ?$

Question Number 124372 Answers: 1 Comments: 0

How many six-digit numbers contain exactly six different digits?

$H o w m a n y s i x - d i g i t n u m b e r s c o n t a i n$ $e x a c t l y s i x d i f f e r e n t d i g i t s ?$

Question Number 124237 Answers: 1 Comments: 1

How many 6 digit odd numbers have different digits?

$H o w m a n y 6 d i g i t o d d n u m b e r s h a v e$ $d i f f e r e n t d i g i t s ?$

Question Number 124173 Answers: 1 Comments: 0

Question Number 123878 Answers: 1 Comments: 0

Nine chairs in a row are to be occupied by six students and Prof George , Prof Pieter, and Prof John. These three professors arrive before the six students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professor George , Pieter and John choose their chairs ?

$N i n e c h a i r s i n a r o w a r e t o b e o c c u p i e d b y$ $s i x s t u d e n t s a n d P r o f G e o r g e, P r o f P i e t e r,$ $a n d P r o f J o h n . T h e s e t h r e e p r o f e s s o r s a r r i v e$ $b e f o r e t h e s i x s t u d e n t s a n d d e c i d e t o c h o o s e$ $t h e i r c h a i r s s o t h a t e a c h p r o f e s s o r w i l l b e b e t w e e n$ $t w o s t u d e n t s . I n h o w m a n y w a y s c a n P r o f e s s o r G e o r g e$ $, P i e t e r a n d J o h n c h o o s e t h e i r c h a i r s ?$

Question Number 123695 Answers: 1 Comments: 0

There are how many ways to answer 5 out of 7 multiple choice question with 5 choices?

$There are how many ways to answer$ $5 out of 7 multiple choice question with$ $5 choices ?$

Question Number 123577 Answers: 1 Comments: 0

Question Number 122250 Answers: 1 Comments: 0

Question Number 121829 Answers: 1 Comments: 0

Question Number 121851 Answers: 0 Comments: 1

How many ways to arrange letters using letters in the word OKINKO (a) 1260 (b) 1160 (c) 980 (d) 880 (e) 720

$H o w m a n y w a y s t o a r r a n g e l e t t e r s$ $u s i n g l e t t e r s i n t h e w o r d O K I N K O$ $(a) 1260 (b) 1160 (c) 980$ $(d) 880 (e) 720$

Question Number 120954 Answers: 0 Comments: 0

shown that n!=Σ_(k=0) ^n (−1)^k (_( k) ^( n) )(n−k)^n please help me

$s h o w n t h a t$ $n! = \underset{k = 0}{\sum^{n}} {(- 1)}^{k} (_{k}^{n}) {(n - k)}^{n}$ $p l e a s e h e l p m e$

Question Number 120431 Answers: 1 Comments: 2

Question Number 120209 Answers: 1 Comments: 0

Peter has 12 relatives (5 man & 7 woman) and his wife also has 12 relatives (5 woman &7 man). They do not have common relatives. They decided to invite 12 guests ,six each of their relatives, such that there are six man and six woman among the guests. How many ways can they choose 12 guests?

$P e t e r h a s 12 r e l a t i v e s (5 m a n & 7 w o m a n)$ $a n d h i s w i f e a l s o h a s 12 r e l a t i v e s$ $(5 w o m a n & 7 m a n) . T h e y d o n o t$ $h a v e c o m m o n r e l a t i v e s . T h e y d e c i d e d$ $t o i n v i t e 12 g u e s t s, s i x e a c h o f$ $t h e i r r e l a t i v e s, s u c h t h a t t h e r e$ $a r e s i x m a n a n d s i x w o m a n$ $a m o n g t h e g u e s t s . H o w m a n y$ $w a y s c a n t h e y c h o o s e 12 g u e s t s ?$

Question Number 120188 Answers: 0 Comments: 0

Let n be a positive integer . Prove that Σ_(k=0) ^n 2^k ((n),(k) ) ((( n−k)),((⌊((n−k)/2)⌋)) ) = (((2n+1)),(( n)) )

$L e t n b e a p o s i t i v e i n t e g e r .$ $P r o v e t h a t \underset{k = 0}{\sum^{n}} 2^{k} (\begin{matrix} n \\ k \end{matrix}) (\begin{matrix} n - k \\ ⌊ \frac{n - k}{2} ⌋ \end{matrix}) = (\begin{matrix} 2 n + 1 \\ n \end{matrix})$

Question Number 120090 Answers: 0 Comments: 0

Find the number of subsets of { 1,2,3,...,2000 } the sum of whose elements is divisible by 5

$F i n d t h e n u m b e r o f s u b s e t s o f$ ${1, 2, 3, . . ., 2000} t h e s u m o f$ $w h o s e e l e m e n t s i s d i v i s i b l e b y 5$

Question Number 119896 Answers: 2 Comments: 1

Question Number 119747 Answers: 1 Comments: 0

Suppose that 7 blue balls , 8 red balls and 9 green balls should be put into three boxes labeled 1,2 and 3, so that any box contains at least one balls of each colour. How many ways can this arrangement be done?

$S u p p o s e t h a t 7 b l u e b a l l s, 8 r e d b a l l s a n d 9 g r e e n$ $b a l l s s h o u l d b e p u t i n t o t h r e e b o x e s l a b e l e d$ $1, 2 a n d 3, s o t h a t a n y b o x c o n t a i n s a t l e a s t$ $o n e b a l l s o f e a c h c o l o u r . H o w m a n y w a y s$ $c a n t h i s a r r a n g e m e n t b e d o n e ?$

Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12 Pg 13 Pg 14 Pg 15

Contact: info@tinkutara.com