Owennjiiidn
Answered

IDNStudy.com, ang iyong platform ng sanggunian para sa malinaw na mga sagot. Ang aming komunidad ay handang magbigay ng malalim at praktikal na mga solusyon sa lahat ng iyong mga katanungan.

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

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[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?

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

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

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

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[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.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#CarryOnLearning

Salamat sa iyong pakikilahok. Patuloy na magbahagi ng iyong mga ideya at kasagutan. Sama-sama tayong magpapaunlad ng isang komunidad ng karunungan at pagkatuto. Salamat sa pagbisita sa IDNStudy.com. Bumalik ka ulit para sa mga sagot sa iyong mga katanungan.