Permutation and Combination – Page 17

Question-54286

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Question Number 54286 by Tinkutara last updated on 01/Feb/19 Commented by Tinkutara last updated on 01/Feb/19 Answers 4d 5b Commented by mr W last updated on 05/Feb/19…

C-4-4-C-4-5-C-4-6-C-4-26-

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Question Number 185350 by cortano1 last updated on 20/Jan/23 $C_{4}^{4} + C_{4}^{5} + C_{4}^{6} + \dots + C_{4}^{26} = ?$ Commented by mr W last…

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-arrangeme

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Question Number 119747 by benjo_mathlover last updated on 26/Oct/20 $S u p p o s e t h a t 7 b l u e b a l l s, 8 r e d b a l l s a n d 9 g r e e n$ $b a l l s s h o u l d b e p u t i n t o t h r e e b o x e s l a b e l e d$ $1, 2 a n d 3, s o t h a t a n y b o x c o n t a i n s a t l e a s t$ $o n e b a l l s o f e a c h c o l o u r . H o w m a n y w a y s$ $c a n t h i s a r r a n g e m e n t b e d o n e ?$ Answered by mr W last…

Question-119733

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Question Number 119733 by bemath last updated on 26/Oct/20 Commented by bemath last updated on 26/Oct/20 $m a n y c h o i c e s o f a {p e r s o n}^{'} s p a t h$ $f r o m A t o B$ Commented by MJS_new last…

k-1-cos-x-2-k-

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Question Number 119479 by 675480065 last updated on 24/Oct/20 $\underset{k = 1}{\prod^{\infty}} \cos (\frac{x}{2^{k}}) = ?$ Answered by Olaf last updated on 25/Oct/20 $\sin 2 θ = 2 \sin θ \cos θ$ $$\mathrm{cos}\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{sin2}\theta}{\mathrm{sin}\theta},\:\theta\:\neq\:{k}\pi…

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-

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Question Number 119397 by bemath last updated on 24/Oct/20 $F i n d t h e n u m b e r o f p o s s i b l e a r r a n g e m e n t s$ $o f t h e l e t t e r s i n t h e w o r d P E N C I L S i f$ $(a)^{'} E^{'} i s n e x t t o^{'} I^{'}$ $(b) E c o m e s b e f o r e I$ $(c) t h e r e a r e t h r e e l e t t e r s b e t w e e n E a n d I$ Commented by liberty last updated…

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-d

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Question Number 119390 by mr W last updated on 24/Oct/20 $w e h a v e 15 d i f f e r e n t m a t h e m a t i c s$ $b o o k s, 10 d i f f e r e n t p h y s i c s b o o k s a n d$ $12 d i f f e r e n t c h e m i s t r y b o o k s . w e s h o u l d$ $c h o o s e 6 b o o k s s u c h t h a t t h e y c o n t a i n$ $a l l t h r e e k i n d s o f b o o k s .$ $i n h o w m a n y w a y s c a n w e d o t h i s ?$ Answered by…

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-al

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Question Number 119364 by bobhans last updated on 24/Oct/20 $S u p p o s e o n c e m o r e {w e}^{'} r e a s k e d$ $t o c h o o s e f o u r s t u d e n t s f r o m h i g h s c h o o l$ $c l a s s o f 15 t o f o r m a c o m m i t t e e$ $b u t t h i s t i m e w e h a v e a r e s t r i c t i o n$ $: w e {d o n}^{'} t w a n t t o c o m m i t t e e t o$ $c o n s i s t o f a l l s e n i o r s o r a l l j u n i o r s$ $. s u p p o s e t h e r e a r e e i g h t s e n i o r s$ $${and}\:{seven}\:{juniors}\:{in}\:{the}\:{class}.\:{How}\:{many} \…

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

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Question Number 118822 by Don08q last updated on 20/Oct/20 $In how many ways can the letters of$ $the word L E V I T A T E be arranged if$ $the vowels must not be next to each$ $other$ Answered by benjo_mathlover last updated on 20/Oct/20…

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-

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Question Number 118694 by benjo_mathlover last updated on 19/Oct/20 $H o w m a n y s e t s o f 3 n u m b e r s e a c h c a n$ $b e f o r m e d f r o m t h e n u m b e r s {1, 2, 3, \dots, 20} i f n o$ $t w o c o n s e c u t i v e n u m b e r s a r e t o b e i n a s e t ?$ Answered by bemath last updated on 19/Oct/20 $$\Rightarrow\: $(\begin{matrix} 18 \\ 3 \end{matrix})$ \:=\:\frac{\mathrm{18}×\mathrm{17}×\mathrm{16}}{\mathrm{3}×\mathrm{2}×\mathrm{1}}\:=\:\mathrm{3}×\mathrm{17}×\mathrm{16}=\mathrm{816} \…

Category: Permutation and Combination