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Permutation and CombinationQuestion and Answers: Page 12

Question Number 119733 Answers: 1 Comments: 5

Question Number 119479 Answers: 3 Comments: 0

Π_(k=1) ^∞ cos((x/2^k )) = ?

$\underset{k = 1}{\prod^{\infty}} \cos (\frac{x}{2^{k}}) = ?$

Question Number 119397 Answers: 2 Comments: 1

Find the number of possible arrangements of the letters in the word PENCILS if (a) ′E′ is next to ′I′ (b) E comes before I (c) there are three letters between E and I

$F i n d t h e n u m b e r o f p o s s i b l e a r r a n g e m e n t s$ $o f t h e l e t t e r s i n t h e w o r d P E N C I L S i f$ $(a)^{'} E^{'} i s n e x t t o^{'} I^{'}$ $(b) E c o m e s b e f o r e I$ $(c) t h e r e a r e t h r e e l e t t e r s b e t w e e n E a n d I$

Question Number 119390 Answers: 2 Comments: 0

we have 15 different mathematics books, 10 different physics books and 12 different chemistry books. we should choose 6 books such that they contain all three kinds of books. in how many ways can we do this?

$w e h a v e 15 d i f f e r e n t m a t h e m a t i c s$ $b o o k s, 10 d i f f e r e n t p h y s i c s b o o k s a n d$ $12 d i f f e r e n t c h e m i s t r y b o o k s . w e s h o u l d$ $c h o o s e 6 b o o k s s u c h t h a t t h e y c o n t a i n$ $a l l t h r e e k i n d s o f b o o k s .$ $i n h o w m a n y w a y s c a n w e d o t h i s ?$

Question Number 119364 Answers: 2 Comments: 0

Suppose once more we′re asked to choose four students from high school class of 15 to form a committee but this time we have a restriction : we don′t want to committee to consist of all seniors or all juniors .suppose there are eight seniors and seven juniors in the class. How many different committe can we form?

$S u p p o s e o n c e m o r e {w e}^{'} r e a s k e d$ $t o c h o o s e f o u r s t u d e n t s f r o m h i g h s c h o o l$ $c l a s s o f 15 t o f o r m a c o m m i t t e e$ $b u t t h i s t i m e w e h a v e a r e s t r i c t i o n$ $: w e {d o n}^{'} t w a n t t o c o m m i t t e e t o$ $c o n s i s t o f a l l s e n i o r s o r a l l j u n i o r s$ $. s u p p o s e t h e r e a r e e i g h t s e n i o r s$ $a n d s e v e n j u n i o r s i n t h e c l a s s . H o w m a n y$ $d i f f e r e n t c o m m i t t e c a n w e f o r m ?$

Question Number 118822 Answers: 2 Comments: 0

In how many ways can the letters of the word LEVITATE be arranged if the vowels must not be next to each other

$In how many ways can the letters of$ $the word L E V I T A T E be arranged if$ $the vowels must not be next to each$ $other$

Question Number 118694 Answers: 2 Comments: 0

How many sets of 3 numbers each can be formed from the numbers { 1,2,3,...,20 } if no two consecutive numbers are to be in a set ?

$H o w m a n y s e t s o f 3 n u m b e r s e a c h c a n$ $b e f o r m e d f r o m t h e n u m b e r s {1, 2, 3, . . ., 20} i f n o$ $t w o c o n s e c u t i v e n u m b e r s a r e t o b e i n a s e t ?$

Question Number 118555 Answers: 2 Comments: 0

Question Number 118489 Answers: 2 Comments: 0

(1) solve the equation ((x−49)/(50)) + ((x−50)/(49)) = ((49)/(x−50)) + ((50)/(x−49)) (2) How many numbers from 12 to 12345 inclusive have digits which are consecutive an in increasing order, reading from left to right ?

$(1) s o l v e t h e e q u a t i o n \frac{x - 49}{50} + \frac{x - 50}{49} = \frac{49}{x - 50} + \frac{50}{x - 49}$ $(2) H o w m a n y n u m b e r s f r o m 12 t o 12345$ $i n c l u s i v e h a v e d i g i t s w h i c h a r e$ $c o n s e c u t i v e a n i n i n c r e a s i n g o r d e r,$ $r e a d i n g f r o m l e f t t o r i g h t ?$

Question Number 117708 Answers: 2 Comments: 3

Find the number of all 5 digit numbers x_1 x_2 x_3 x_4 x_5 with x_1 ≥x_2 ≥x_3 ≥x_4 ≥x_5 .

$F i n d t h e n u m b e r o f a l l 5 d i g i t$ $n u m b e r s x_{1} x_{2} x_{3} x_{4} x_{5} w i t h$ $x_{1} ⩾ x_{2} ⩾ x_{3} ⩾ x_{4} ⩾ x_{5} .$

Question Number 117281 Answers: 1 Comments: 0

In how many different ways can we select 5 numbers from 9 numbers {1,2,3,...,9}? A number may be selected more than one time.

$I n h o w m a n y d i f f e r e n t w a y s c a n w e$ $s e l e c t 5 n u m b e r s f r o m 9 n u m b e r s$ ${1, 2, 3, . . ., 9} ?$ $A n u m b e r m a y b e s e l e c t e d m o r e t h a n$ $o n e t i m e .$

Question Number 117192 Answers: 1 Comments: 0

Assuming you have enough coins of 1,5,10,25,and 50cents. In how many ways can you make a change for 1dollar.

$Assuming you have enough coins$ $of 1, 5, 10, 25, and 50 cents . In how$ $many ways can you make a change for 1 dollar .$

Question Number 116883 Answers: 1 Comments: 0

Find the number m of ways to partition 10 students into four team so that two team contains 3 students and two team contains 2 students .

$Find the number m of ways to$ $partition 10 students into four team$ $so that two team contains 3 students$ $and two team contains 2 students .$

Question Number 116881 Answers: 3 Comments: 0

Find the number m of non negative integer solution of x+y+z=18

$Find the number m of non negative$ $integer solution of x + y + z = 18$

Question Number 116397 Answers: 2 Comments: 0

The number 1,2,3,4,...,7 are randomly divided into two non −empty subsets. The probability that the sum of the numbers in the two subsets being equal is (r/s) expressed in the lowest term. Find r+s ?

$T h e n u m b e r 1, 2, 3, 4, . . ., 7 a r e r a n d o m l y$ $d i v i d e d i n t o t w o n o n - e m p t y s u b s e t s .$ $T h e p r o b a b i l i t y t h a t t h e s u m o f t h e$ $n u m b e r s i n t h e t w o s u b s e t s b e i n g$ $e q u a l i s \frac{r}{s} e x p r e s s e d i n t h e l o w e s t$ $t e r m . F i n d r + s ?$

Question Number 116360 Answers: 1 Comments: 0

A five digits number divisible by 3 is to be formed using the number 0,1,2,3,4 and 5 without repetition The total number of ways this can be done is __

$A five digits number divisible by 3$ $is to be formed using the number$ $0, 1, 2, 3, 4 and 5 without repetition$ $The total number of ways this can$ $be done is__$

Question Number 116177 Answers: 0 Comments: 1

Question Number 115988 Answers: 1 Comments: 2

Question Number 115902 Answers: 0 Comments: 0

The secret number is made from the numbers 1,2,2,3,3,4,5. Many secret numbers can be created if the same number is not adjacent except in the first two place is _ (a)1142 (b) 1212 (c) 1246 (d) 1248 (e) 1250

$T h e s e c r e t n u m b e r i s m a d e f r o m$ $t h e n u m b e r s 1, 2, 2, 3, 3, 4, 5 .$ $M a n y s e c r e t n u m b e r s c a n b e c r e a t e d$ $i f t h e s a m e n u m b e r i s n o t a d j a c e n t$ $e x c e p t i n t h e f i r s t t w o p l a c e i s_$ $(a) 1142 (b) 1212 (c) 1246$ $(d) 1248 (e) 1250$

Question Number 115769 Answers: 1 Comments: 0

There are 3 teachers and 6 students who will sit on the 9 available seats. many arrangements they sit if each teacher is flanked by 2 students

$T h e r e a r e 3 t e a c h e r s a n d 6 s t u d e n t s$ $w h o w i l l s i t o n t h e 9 a v a i l a b l e s e a t s . m a n y$ $a r r a n g e m e n t s t h e y s i t i f e a c h$ $t e a c h e r i s f l a n k e d b y 2 s t u d e n t s$

Question Number 115408 Answers: 1 Comments: 0

how many 6 digit numbers exist which are divisible by 11 and have no repeating digits?

$h o w m a n y 6 d i g i t n u m b e r s e x i s t$ $w h i c h a r e d i v i s i b l e b y 11 a n d h a v e n o$ $r e p e a t i n g d i g i t s ?$

Question Number 115387 Answers: 0 Comments: 6

Question Number 115230 Answers: 0 Comments: 6

2 women and 4 men will sit on the 8 available seats and surround the round table . The many possible arrangements of them sitting if they sat randomly

$2 w o m e n a n d 4 m e n w i l l s i t o n t h e$ $8 a v a i l a b l e s e a t s a n d s u r r o u n d$ $t h e r o u n d t a b l e . T h e m a n y p o s s i b l e$ $a r r a n g e m e n t s o f t h e m s i t t i n g$ $i f t h e y s a t r a n d o m l y$

Question Number 115170 Answers: 3 Comments: 0

(1)Given ((P _(n−1)^(2n+1) )/(P _n^(2n−1) )) = (3/5) , find n = ? (2) in how many ways can 6 persons stand in a queue? (3) how many different 4 letter words can be formed by using letters of EDUCATION using each letter at most once ?

$(1) G i v e n \frac{P_{n - 1}^{2 n + 1}}{P_{n}^{2 n - 1}} = \frac{3}{5}, f i n d n = ?$ $(2) i n h o w m a n y w a y s c a n 6 p e r s o n s$ $s t a n d i n a q u e u e ?$ $(3) h o w m a n y d i f f e r e n t 4 l e t t e r w o r d s$ $c a n b e f o r m e d b y u s i n g l e t t e r s o f$ $E D U C A T I O N u s i n g e a c h l e t t e r a t$ $m o s t o n c e ?$

Question Number 114797 Answers: 1 Comments: 0

There are 6 people going to sit in a circle . The number of arrangements they sit if there are 2 people who always sit next to each other

$T h e r e a r e 6 p e o p l e g o i n g t o s i t i n$ $a c i r c l e . T h e n u m b e r o f a r r a n g e m e n t s$ $t h e y s i t i f t h e r e a r e 2 p e o p l e w h o$ $a l w a y s s i t n e x t t o e a c h o t h e r$

Question Number 113710 Answers: 1 Comments: 2

you have 2 identical mathematics books, 2 identical physics books, 2 identical chemistry books, 2 identical biology books and 2 geography books. in how many ways can you compile these books such that same books are not mutually adjacent?

$y o u h a v e 2 i d e n t i c a l m a t h e m a t i c s$ $b o o k s, 2 i d e n t i c a l p h y s i c s b o o k s, 2$ $i d e n t i c a l c h e m i s t r y b o o k s, 2 i d e n t i c a l$ $b i o l o g y b o o k s a n d 2 g e o g r a p h y b o o k s .$ $i n h o w m a n y w a y s c a n y o u c o m p i l e$ $t h e s e b o o k s s u c h t h a t s a m e b o o k s$ $a r e n o t m u t u a l l y a d j a c e n t ?$

Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12 Pg 13 Pg 14 Pg 15 Pg 16

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