Answered

Magtanong at makakuha ng eksaktong mga sagot sa IDNStudy.com. Ang aming mga eksperto ay handang magbigay ng malalim na sagot at praktikal na solusyon sa lahat ng iyong mga tanong.

B. In how many ways can a committee of 5 be selected from a group of 10 individuals? A 107 B. 178 C 180 D. 252 8. ​

Sagot :

UK2019idn

✏️COMBINATIONS

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

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

  • In how many ways can a committee of 5 be selected from a group of 10 individuals?

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

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

[tex] \qquad\:\:\Large\rm» \:\: \green{D. \: 252} [/tex]

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

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

» Find the number of ways in which 5 committees are selected out of 10 individuals per group.

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

  • [tex] \begin{aligned} \rm _{10}C_5 = \frac{10!}{5!(10 - 5)!} \end{aligned} [/tex]

  • [tex] \begin{aligned} \rm _{10}C_5 = \frac{10!}{5! \ 5!} \end{aligned} [/tex]

  • [tex] \begin{aligned} \rm _{10}C_5 = \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot \cancel{5!}}{5 \cdot 4 \cdot 3 \cdot 2 \cdot \cancel{5!}} \end{aligned} [/tex]

  • [tex]\begin{aligned} \rm _{10}C_5 = \frac{ \cancel{10}^{ \: 2} \cdot 9 \cdot \cancel{ \: 8 \: }^{ \: 2} \cdot 7 \cdot \cancel{ \: 6 \: }}{\cancel{ \: 5 \: } \cdot \cancel{ \:4 \: } \cdot \cancel{ \: 3 \: } \cdot \cancel{ \: 2 \: }} \end{aligned}[/tex]

  • [tex]\rm _{10}C_5 = 2 \cdot 9 \cdot 2 \cdot 7[/tex]

  • [tex]\rm _{10}C_5 = 252[/tex]

[tex] \therefore [/tex] There are 252 ways to select 5 committees from the group of 10 individuals.

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

#CarryOnLearning

Pinahahalagahan namin ang bawat tanong at sagot na iyong ibinabahagi. Huwag kalimutang bumalik at magtanong ng mga bagong bagay. Sama-sama tayong magtatagumpay. Ang IDNStudy.com ang iyong mapagkakatiwalaang mapagkukunan ng mga sagot. Salamat at bumalik ka ulit.