Jade9044viz
Answered

how many 5 digits number can be formed from digits 2,3,4,5,6, and 8?​

Sagot :

AGboiiviz

[tex] \large\underline \mathcal{{QUESTION:}}[/tex]

how many 5 digits number can be formed from digits 2,3,4,5,6, and 8?

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[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]

» 2,3,4,5,6,8 are 6 objects

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  • Given that n = 6 and r = 5

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

[tex]\sf{P(6,5)=\frac{6!}{(6-5)!}}[/tex]

[tex]\sf{P(6,5)=\frac{6!}{1!}}[/tex]

[tex]\sf{P(6,5)=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{1}}[/tex]

[tex]\sf{P(6,5) = 720}[/tex]

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[tex] \large\underline \mathcal{{ANSWER:}}[/tex]

  • There are 720 ways
Chaser27viz

[tex] \footnotesize \begin {aligned} \bold{\textsf{Variation Formula :} }\\ \sf \: V_k(n)=\frac{n!}{(n-k)!}\\ \\ \sf \: n = 6 \\ \sf \: k = 5 \\ \\ \sf \: V_5(6)=\frac{6!}{(6-5)!} = \frac{6}{1} \\ \\ \sf \frac{6 \times 5 \times 4 \times 3 \times 2 \times \cancel1}{ \times \cancel 1} = 720 \\ \\ \boxed{\textsf{720 \: ways}}\end{aligned}[/tex]