Question and Answers Forum

All Questions   Topic List

Permutation and CombinationQuestion and Answers: Page 1

Question Number 218169    Answers: 0   Comments: 0

P(5,6)=((15!)/((15−6))) = ((15!)/(9!)) =((15×14×131×2×11×10×9×8×7×6×5×4×3×2×1)/(9×8×7×6×5×4×3×2×)) =15×14×13×12×11×10 =3,603,600

$${P}\left(\mathrm{5},\mathrm{6}\right)=\frac{\mathrm{15}!}{\left(\mathrm{15}−\mathrm{6}\right)}\:=\:\frac{\mathrm{15}!}{\mathrm{9}!}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{15}×\mathrm{14}×\mathrm{131}×\mathrm{2}×\mathrm{11}×\mathrm{10}×\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}}{\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{15}×\mathrm{14}×\mathrm{13}×\mathrm{12}×\mathrm{11}×\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3},\mathrm{603},\mathrm{600} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 218129    Answers: 2   Comments: 0

how many different words can be formed from the word MATHEMATICS? note: here a word should have at least two letters, but mustn′t have a meaning.

$${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{from}\:{the}\:{word}\: \\ $$$$\boldsymbol{\mathrm{MATHEMATICS}}? \\ $$$${note}:\:\:{here}\:{a}\:{word}\:{should}\:{have}\:{at}\: \\ $$$${least}\:{two}\:{letters},\:{but}\:{mustn}'{t}\:{have}\:{a} \\ $$$${meaning}. \\ $$

Question Number 217402    Answers: 3   Comments: 0

Question Number 214923    Answers: 0   Comments: 0

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=?

$$\:\:\frac{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{0}}\end{pmatrix}\:+\mathrm{3}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{5}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{2}}\end{pmatrix}\:+...+\left(\mathrm{2n}+\mathrm{1}\right)\begin{pmatrix}{\mathrm{n}}\\{\mathrm{n}}\end{pmatrix}}{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{2}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{2}}\end{pmatrix}\:+\:\mathrm{3}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{3}}\end{pmatrix}\:+...+\mathrm{n}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{n}}\end{pmatrix}}\:=\frac{\mathrm{23}}{\mathrm{11}} \\ $$$$\:\mathrm{n}=? \\ $$

Question Number 208263    Answers: 1   Comments: 0

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

s

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

Question Number 206323    Answers: 0   Comments: 0

Question Number 206156    Answers: 1   Comments: 4

Question Number 205683    Answers: 1   Comments: 0

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

Question Number 205690    Answers: 0   Comments: 3

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?

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

Question Number 203198    Answers: 0   Comments: 0

Question Number 202598    Answers: 2   Comments: 0

Question Number 202584    Answers: 1   Comments: 0

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

Question Number 202374    Answers: 1   Comments: 2

  Pg 1      Pg 2      Pg 3      Pg 4      Pg 5      Pg 6      Pg 7      Pg 8      Pg 9      Pg 10   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com