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Question Number 94816 by i jagooll last updated on 21/May/20

Commented by i jagooll last updated on 21/May/20

Commented by i jagooll last updated on 21/May/20

yes sir. my answer is wrong

$$\mathrm{yes}\:\mathrm{sir}.\:\mathrm{my}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{wrong} \\ $$

Answered by mr W last updated on 21/May/20

possibilities total: 12! possibilities that students of class B don′t stand next to each other: C_5 ^8 ×5!×7!=33 868 800 probalility p=((C_5 ^8 ×5!×7!)/(12!))=(7/(99))

$${possibilities}\:{total}:\:\mathrm{12}! \\ $$$${possibilities}\:{that}\:{students}\:{of}\:{class}\:{B} \\ $$$${don}'{t}\:{stand}\:{next}\:{to}\:{each}\:{other}: \\ $$$${C}_{\mathrm{5}} ^{\mathrm{8}} ×\mathrm{5}!×\mathrm{7}!=\mathrm{33}\:\mathrm{868}\:\mathrm{800} \\ $$$${probalility}\:{p}=\frac{{C}_{\mathrm{5}} ^{\mathrm{8}} ×\mathrm{5}!×\mathrm{7}!}{\mathrm{12}!}=\frac{\mathrm{7}}{\mathrm{99}} \\ $$

Commented by i jagooll last updated on 21/May/20

how get C_5 ^8 sir?

$$\mathrm{how}\:\mathrm{get}\:\mathrm{C}_{\mathrm{5}} ^{\mathrm{8}} \:\mathrm{sir}? \\ $$

Commented by mr W last updated on 21/May/20

if we have 5 red balls and 7 blues balls and we place them in a line such that no red balls are next to each other. how many ways? certainly much more than 3, i think.

$${if}\:{we}\:{have}\:\mathrm{5}\:{red}\:{balls}\:{and}\:\mathrm{7}\:{blues} \\ $$$${balls}\:{and}\:{we}\:{place}\:{them}\:{in}\:{a}\:{line} \\ $$$${such}\:{that}\:{no}\:{red}\:{balls}\:{are}\:{next}\:{to} \\ $$$${each}\:{other}.\:{how}\:{many}\:{ways}?\:{certainly} \\ $$$${much}\:{more}\:{than}\:\mathrm{3},\:{i}\:{think}. \\ $$

Commented by i jagooll last updated on 21/May/20

Commented by i jagooll last updated on 21/May/20

i got it sir

$$\mathrm{i}\:\mathrm{got}\:\mathrm{it}\:\mathrm{sir} \\ $$

Commented by mr W last updated on 21/May/20

how did you get 3×5!×7!?

$${how}\:{did}\:{you}\:{get}\:\mathrm{3}×\mathrm{5}!×\mathrm{7}!? \\ $$

Commented by prakash jain last updated on 21/May/20

7 students provide 8 possibilities for class B student to occupo −A−A−A−A−A−A−A− − are spaces available for class B.

$$\mathrm{7}\:\mathrm{students}\:\mathrm{provide}\:\mathrm{8}\:\mathrm{possibilities} \\ $$$$\mathrm{for}\:\mathrm{class}\:\mathrm{B}\:\mathrm{student}\:\mathrm{to}\:\mathrm{occupo} \\ $$$$−\mathrm{A}−\mathrm{A}−\mathrm{A}−\mathrm{A}−\mathrm{A}−\mathrm{A}−\mathrm{A}− \\ $$$$−\:\mathrm{are}\:\mathrm{spaces}\:\mathrm{available}\:\mathrm{for}\:\mathrm{class}\:\mathrm{B}. \\ $$

Commented by mr W last updated on 21/May/20

how i solved: students from class B must be separated by at least one student from class A. so we arrange at first the students from class A, there are 7! ways. □A□A□A□A□A□A□A□ now we place the students from class B. they can be placed in the positions □. from these 8 possible positions we select 5 from students of class B, there are C_5 ^8 ways. to arrange these 5 students in the selected 5 positions there are 5! ways. therefore the total possibilities to arrange the 12 students such that no students from class B are next to each other are 7!×C_5 ^8 ×5!.

$${how}\:{i}\:{solved}: \\ $$$${students}\:{from}\:{class}\:{B}\:{must}\:{be}\:{separated} \\ $$$${by}\:{at}\:{least}\:{one}\:{student}\:{from}\:{class}\:{A}. \\ $$$${so}\:{we}\:{arrange}\:{at}\:{first}\:{the}\:{students} \\ $$$${from}\:{class}\:{A},\:{there}\:{are}\:\mathrm{7}!\:{ways}. \\ $$$$\Box\boldsymbol{{A}}\Box\boldsymbol{{A}}\Box\boldsymbol{{A}}\Box\boldsymbol{{A}}\Box\boldsymbol{{A}}\Box\boldsymbol{{A}}\Box\boldsymbol{{A}}\Box \\ $$$${now}\:{we}\:{place}\:{the}\:{students}\:{from}\:{class} \\ $$$${B}.\:{they}\:{can}\:{be}\:{placed}\:{in}\:{the}\:{positions} \\ $$$$\Box.\:{from}\:{these}\:\mathrm{8}\:{possible}\:{positions}\:{we} \\ $$$${select}\:\mathrm{5}\:{from}\:{students}\:{of}\:{class}\:{B}, \\ $$$${there}\:{are}\:{C}_{\mathrm{5}} ^{\mathrm{8}} \:{ways}.\:{to}\:{arrange}\:{these}\:\mathrm{5} \\ $$$${students}\:{in}\:{the}\:{selected}\:\mathrm{5}\:{positions} \\ $$$${there}\:{are}\:\mathrm{5}!\:{ways}.\:{therefore}\:{the} \\ $$$${total}\:{possibilities}\:{to}\:{arrange}\:{the} \\ $$$$\mathrm{12}\:{students}\:{such}\:{that}\:{no}\:{students} \\ $$$${from}\:{class}\:{B}\:{are}\:{next}\:{to}\:{each}\:{other} \\ $$$${are}\:\mathrm{7}!×{C}_{\mathrm{5}} ^{\mathrm{8}} ×\mathrm{5}!. \\ $$

Commented by i jagooll last updated on 21/May/20

yes sir. it right

$$\mathrm{yes}\:\mathrm{sir}.\:\mathrm{it}\:\mathrm{right} \\ $$

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