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Permutation and CombinationQuestion and Answers: Page 25

Question Number 3273 Answers: 3 Comments: 0

∗ ∗ ∗ ∗ One can only move to the ∗ ∗ ∗ ∗ right or downwards on the ∗ ∗ ∗ ∗ 4 by 6 point lattice shown. ∗ ∗ ∗ ∗ How many paths from ∗ to ∗ ∗ ∗ ∗ ∗ are there? ∗ ∗ ∗ ∗

$* * * * O n e c a n o n l y m o v e t o t h e$ $* * * * r i g h t o r d o w n w a r d s o n t h e$ $* * * * 4 b y 6 p o i n t l a t t i c e s h o w n .$ $* * * * H o w m a n y p a t h s f r o m * t o$ $* * * * * a r e t h e r e ?$ $* * * *$

Question Number 3216 Answers: 1 Comments: 0

You have unlimited number of 1kg, 5kg 10kg and 25 kg weights. In how many ways you can create a total of 43kg. For example 43×1 5×8+3×2 etc.

$You have unlimited number of 1 kg, 5 kg$ $10 kg and 25 kg weights . In how many ways$ $you can create a total of 43 kg .$ $For example$ $43 \times 1$ $5 \times 8 + 3 \times 2$ $etc .$

Question Number 1468 Answers: 1 Comments: 0

Question Number 1074 Answers: 0 Comments: 3

Prove by induction the following result where N is a positive even integer. S_1 ^2 +S_2 ^2 =2^N where S_1 =Σ_(r=1) ^((N/2)+1) (−1)^(r−1) ((N),((2(r−1))) ) and S_2 =Σ_(r=1) ^(N/2) (−1)^(r+1) ((N),((2r−1)) ) .

$P r o v e b y i n d u c t i o n t h e f o l l o w i n g r e s u l t w h e r e N i s a p o s i t i v e e v e n i n t e g e r .$ $S_{1}^{2} + S_{2}^{2} = 2^{N}$ $w h e r e S_{1} = \underset{r = 1}{\sum^{\frac{N}{2} + 1}} {(- 1)}^{r - 1} (\begin{matrix} N \\ 2 (r - 1) \end{matrix}) a n d S_{2} = \underset{r = 1}{\sum^{N / 2}} {(- 1)}^{r + 1} (\begin{matrix} N \\ 2 r - 1 \end{matrix}) .$

Question Number 921 Answers: 0 Comments: 0

How many arrays of the letters of the word BELMOPAN are possible if no two vowels come together?

$H o w m a n y a r r a y s o f t h e l e t t e r s$ $o f t h e w o r d B E L M O P A N a r e$ $p o s s i b l e i f n o t w o v o w e l s c o m e$ $t o g e t h e r ?$

Question Number 911 Answers: 1 Comments: 0

Eight people are seated around a circular table. Each person must shake everyone′s hand but they must not shake hands with the two persons seated at their sides. How many handshakes occur?

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

Question Number 883 Answers: 1 Comments: 0

How many even numbers between 3000 and 7000 can be formed using the digits 2,3,4,5,6 and 8 if repetition of digits is not allowed?

$H o w m a n y e v e n n u m b e r s$ $b e t w e e n 3000 a n d 7000 c a n b e$ $f o r m e d u s i n g t h e d i g i t s$ $2, 3, 4, 5, 6 a n d 8 i f r e p e t i t i o n$ $o f d i g i t s i s n o t a l l o w e d ?$

Question Number 877 Answers: 0 Comments: 2

An 8×8 checkerboard is to be coloured with 6 colors in a way that no 2 adjacent cells (sharing side) have the same color. In how many ways can it be done.

$An 8 \times 8 checkerboard is to be coloured$ $with 6 colors in a way that no 2 adjacent$ $cells (sharing side) have the same color . In how$ $many ways can it be done .$

Question Number 66 Answers: 0 Comments: 2

How many unique arrangements are possible for a 2×2 Rubic cube?

$How many unique arrangements are$ $possible for a 2 \times 2 Rubic cube ?$

Question Number 23 Answers: 1 Comments: 0

Sum the series Σ_(n=0) ^∞ P_r (n)(x^n /(n!)) , where P_r (n) is a polynomial of degree r in n.

$Sum the series \underset{n = 0}{\sum^{\infty}} P_{r} (n) \frac{x^{n}}{n!}, where P_{r} (n)$ $is a polynomial of degree r in n .$

Pg 20 Pg 21 Pg 22 Pg 23 Pg 24 Pg 25 Pg 26

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