thapasajjal9
Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

permutation:
A college has 7 good badminton players.In how many ways can a team of 5 players be selected??​

Sagot :

Formula for permutation is:

[tex] \boxed{ \tt^{n} C_{r} = \frac{n!}{r!(n - r)!} }[/tex]

Calculation,

Plug in the values:

Required number of ways = ²C7

  • n = 7
  • r = 5

[tex] \sf \frac{7!}{5!(7 - 5)!} [/tex]

[tex] \sf \frac{7 \times 6 \times \cancel{5!}}{ \cancel{5! }\times 2!} [/tex]

[tex] \sf \frac{7 \times 6 }{ 2!} [/tex]

[tex] \sf \frac{42 }{ 2!} [/tex]

[tex] \sf \frac{42 }{ 2} = 21[/tex]

Thus, The players can be selected in 21 different ways!!~

Here one player cannot be repeated so repeating is not allowed.

  • Hence we use combination here

  • n=7
  • r=5

Total ways

[tex]\\ \rm\hookrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

  • Put values

[tex]\\ \rm\hookrightarrow ^7C_5[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7!}{5!(7-5)!}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7!}{5!2!}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7\times 6\times 5!}{5!(2)}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7(6)}{2}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{42}{2}[/tex]

[tex]\\ \rm\hookrightarrow 21ways[/tex]

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.