Tabancura3062idn
Answered

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How many four- letter words can be formed from DESTINY If repetition of a letter is NOT permitted? (note: The words may not mean anything) *

A.2401

B.840

C.220

D.105
with explanation lang po salamat

​

Sagot :

AGboiiidn

[tex] \large\underline{ \bold{ANSWER}}[/tex]

[tex]\textrm{When Repetition is not Allowed}[/tex]

[tex]\longmapsto\rm{P(n,r)= \frac{n!}{(n-r)!}}[/tex]

[tex]\longmapsto\rm{P(7,4)= \frac{7!}{(7-4)!}}[/tex]

[tex]\longmapsto\rm{P(7,4)= \frac{7!}{3!}}[/tex]

[tex]\longmapsto\rm{P(7,4)= \frac{7×6×5×4×3×2×1}{3×2×1}}[/tex]

[tex]\longmapsto\rm{P(7,4)= \frac{7×6×5×4×\cancel{3×2×1}}{\cancel{3×2×1}}}[/tex]

[tex]\longmapsto \rm{P(7,4) = 7×6×5×4}[/tex]

[tex]\longmapsto \boxed{\rm{P(7,4) =840 }}[/tex]

[tex] \large\underline{ \bold{ANSWER}}[/tex]

  • [tex]\text{\underline{OPTION B}(840)}[/tex]
Chaser27idn

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[tex] \large \orange{ \bold{PROBLEM:}}[/tex]

How many four- letter words can be formed from DESTINY If repetition of a letter is NOT permitted? (note: The words may not mean anything) *

[tex] \large \bold{PERMUTATION:}[/tex]

[tex] \bold{DESTINY \:IS \: = 7\: LETTER}[/tex]

[tex] \large \green{ \bold{FORMULA:}}[/tex]

[tex] \bold{P(n,r)= \frac{n!}{(n - r)!}} = ? [/tex]

[tex]\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3mm}\put(1,1){\line(1,0){6.8}}\end{picture}[/tex]

[tex] \bold{N(Objects)=7} \\ \bold{R(Sample)=4}[/tex]

[tex] \bold{P(n,r)=P(7,4)}[/tex]

[tex] \large \bold{ = \frac{7!}{(7 - 4)!} }[/tex]

[tex] \large \dashrightarrow \underline{ \boxed{ \bold{ = 840}}}[/tex]

[tex] \large \bold{7 \times 6 \times 5 \times 4 } \\ \large \bold{ \: \: \: \: \: \: 42 \times5 \times 4} \\ \large \bold{ \: \: \: \: \: \: \: \: \: \: \: \: 210 \times 4} \\ \large \dashrightarrow \underline{ \boxed{ \bold{ \: \: \: \: \: \: \: \: \: \: 840}}}[/tex]

[tex]\purple{\begin{gathered} \gamma \\ \huge \boxed{ \ddot \smile}\end{gathered}} \: \pink{\begin{gathered} \gamma \\ \huge \boxed{ \ddot \smile}\end{gathered}} \: \red{\begin{gathered} \gamma \\ \huge \boxed{ \ddot \smile}\end{gathered}} \: \orange{\begin{gathered} \gamma \\ \huge \boxed{ \ddot \smile}\end{gathered}}[/tex]

[tex] \large \color{indigo}{ \bold{Carry\: On\: Latex}}[/tex]

[tex]\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3mm}\put(1,1){\line(1,0){6.8}}\end{picture}[/tex]

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