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Permutation and CombinationQuestion and Answers: Page 1

Question Number 213796 Answers: 4 Comments: 0

Question Number 212686 Answers: 4 Comments: 4

in how many ways can a teacher divide his 10 studens into 4 groups such that each group has at least 2 students?

$${in}\:{how}\:{many}\:{ways}\:{can}\:{a}\:{teacher} \\ $$$${divide}\:{his}\:\mathrm{10}\:{studens}\:{into}\:\mathrm{4}\:{groups} \\ $$$${such}\:{that}\:{each}\:{group}\:{has}\:{at}\:{least}\:\mathrm{2}\: \\ $$$${students}? \\ $$

Question Number 210290 Answers: 1 Comments: 0

Question Number 209281 Answers: 2 Comments: 2

Find the value of r, if ^(10) C_r = ^(10) C_(2r + 1)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{r},\:\mathrm{if}\:\:\overset{\mathrm{10}} {\:}\mathrm{C}_{\mathrm{r}} \:\:=\:\:\overset{\mathrm{10}} {\:}\mathrm{C}_{\mathrm{2r}\:\:+\:\:\mathrm{1}} \\ $$

Question Number 208662 Answers: 2 Comments: 0

(( ((n),(0) ) +3 ((n),(1) ) +5 ((n),(2) ) +...+(2n+1) ((n),(n) ))/( ((n),(1) ) +2 ((n),(2) ) + 3 ((n),(3) ) +...+n ((n),(n) ))) =((23)/(11)) n=?

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Question Number 208238 Answers: 1 Comments: 0

Show that (π/4) < ∫_0 ^1 (√(1−x^4 ))dx using x = sint show that ∫_0 ^1 (√(1−x^4 ))dx<((2(√2))/3) using (∫_0 ^1 f(x)g(x)dx)^2 <∫_0 ^1 (f(x))^2 dx∫_0 ^1 (g(x))^2 dx

$$\mathrm{S}{how}\:{that} \\ $$$$\frac{\pi}{\mathrm{4}}\:<\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx}\:{using}\:{x}\:=\:{sint} \\ $$$${show}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx}<\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$$${using}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){g}\left({x}\right){dx}\right)^{\mathrm{2}} <\int_{\mathrm{0}} ^{\mathrm{1}} \left({f}\left({x}\right)\right)^{\mathrm{2}} {dx}\int_{\mathrm{0}} ^{\mathrm{1}} \left({g}\left({x}\right)\right)^{\mathrm{2}} {dx} \\ $$

Question Number 207937 Answers: 0 Comments: 0

An ordered data consists of 6 even numbers and 4 odd numbers. The average of the odd numbers is 2022. The 3rd, 5th, 6th and 8 th numbers are odd. The data range is 24 , and the interquartile range is 14. The largest possible average of the ten numbers is ___

$$\:\:\mathrm{An}\:\mathrm{ordered}\:\mathrm{data}\:\mathrm{consists}\:\mathrm{of}\: \\ $$$$\:\mathrm{6}\:\mathrm{even}\:\mathrm{numbers}\:\mathrm{and}\:\mathrm{4}\:\mathrm{odd}\:\mathrm{numbers}. \\ $$$$\:\mathrm{The}\:\mathrm{average}\:\mathrm{of}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{numbers}\: \\ $$$$\:\mathrm{is}\:\mathrm{2022}.\:\mathrm{The}\:\mathrm{3rd},\:\mathrm{5th},\:\mathrm{6th}\:\mathrm{and} \\ $$$$\:\mathrm{8}\:\mathrm{th}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{odd}.\: \\ $$$$\:\mathrm{The}\:\mathrm{data}\:\mathrm{range}\:\mathrm{is}\:\mathrm{24}\:,\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\:\mathrm{interquartile}\:\mathrm{range}\:\mathrm{is}\:\mathrm{14}.\: \\ $$$$\:\mathrm{The}\:\mathrm{largest}\:\mathrm{possible}\:\mathrm{average} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{ten}\:\mathrm{numbers}\:\mathrm{is}\:\_\_\_\: \\ $$

Question Number 207179 Answers: 2 Comments: 0

Question Number 206827 Answers: 0 Comments: 1

log (x) = sin (x) x = ?

$$\mathrm{log}\:\left({x}\right)\:=\:\mathrm{sin}\:\left({x}\right) \\ $$$${x}\:=\:? \\ $$

Question Number 206681 Answers: 3 Comments: 6

$$\:\:\:\cancel{{s}} \\ $$$$ \\ $$

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Question Number 206156 Answers: 1 Comments: 4

Question Number 205683 Answers: 1 Comments: 0

$$\:\:\:\:\: \\ $$

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Question Number 205045 Answers: 0 Comments: 4

$$\:\:\:\:\underbrace{ \underline{}\:} \\ $$

Question Number 203833 Answers: 1 Comments: 0

How many bit strings of length 11 have exactly three consecutive 1s?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{11}\:\mathrm{have} \\ $$$$\mathrm{exactly}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$

Question Number 203832 Answers: 2 Comments: 0

How many bit strings of length 10 do not have four consecutive 1s?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10}\:\mathrm{do}\:\mathrm{not} \\ $$$$\mathrm{have}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$

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Question Number 200051 Answers: 2 Comments: 2

There are many ways to arrange 3 red balls and 9 black balls in a circle so that there are a minimum of 2 black balls between 2 adjacent red balls. (a) 180×8! (b) 240×7! (c) 364×6! (d) 282×4! (e) 144×5!

$$ \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{arrange}\:\mathrm{3}\:\mathrm{red} \\ $$$$\:\mathrm{balls}\:\mathrm{and}\:\mathrm{9}\:\mathrm{black}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{2} \\ $$$$\mathrm{black}\:\mathrm{balls}\:\mathrm{between}\:\mathrm{2}\:\mathrm{adjacent}\:\mathrm{red} \\ $$$$\mathrm{balls}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{180}×\mathrm{8}!\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{240}×\mathrm{7}!\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{364}×\mathrm{6}! \\ $$$$\:\left(\mathrm{d}\right)\:\mathrm{282}×\mathrm{4}!\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{144}×\mathrm{5}!\: \\ $$

Question Number 199337 Answers: 1 Comments: 0

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