thapasajjal9
Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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 choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.