Thapasajjal9idn
Answered

IDNLearn.com provides a collaborative platform for sharing and gaining knowledge. Join our interactive community and get comprehensive, reliable answers to all your questions.

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]

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.