Owennjiiidn
Answered

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how many three digit number can be formed from the numbers 1 4 5 6 7 8 9 if repetition is not allowed? ​

Sagot :

UK2019idn

✏️PERMUTATIONS

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[tex]\underline{\mathbb{PROBLEM:}}[/tex]

  • How many three digit numbers can be formed from the number 1,4,5,6,7,8,9 if repetition is not allowed?

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[tex]\underline{\mathbb{ANSWER:}}[/tex]

[tex]\qquad\LARGE\rm» \:\: \green{210\:ways}[/tex]

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[tex]\underline{\mathbb{SOLUTION:}}[/tex]

- Using the Permutation Formula to identify the number of permutations of ways does 7 numbers picked 3 at a time without repetition.

[tex]\begin{aligned} & \bold{\color{lightblue}Formula:} \\ & \boxed{\: \rm _nP_r = \frac{n!}{(n - r)!} \:}\end{aligned} [/tex]

  • [tex]\begin{aligned} \rm _7P_3 = \frac{7!}{(7 - 3)!} \end{aligned} [/tex]

  • [tex]\begin{aligned} \rm _7P_3 = \frac{7!}{4!} \end{aligned} [/tex]

  • [tex]\begin{aligned} \rm _7P_3 = \frac{7 \cdot 6 \cdot 5 \cdot \cancel{4!}}{ \cancel{4!}} \end{aligned} [/tex]

  • [tex]\rm _7P_3 = 7 \cdot 6 \cdot 5[/tex]

  • [tex]\rm _7P_3 = 210[/tex]

[tex]\therefore[/tex] There are 210 ways to arrange the 7 numbers picked 3 at a time.

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