Respuesta :

fieryanswererft

Answer:

1820 ways

Explanation:

Use combination method. where order does not matter.

[tex]\sf _n C_r=\dfrac{n !}{r ! (n-r) !}[/tex]    : combination formula

Solve:

[tex]\sf \bold{\cdot}} \ _{16} C_4[/tex]

[tex]\sf \bold{ \cdot} \ \dfrac{16!}{4!(16-4)!}[/tex]

[tex]\sf \bold{ \cdot} \ \dfrac{16!}{4! \ x \ 12!}[/tex]

[tex]\sf \bold{ \cdot} \ 1820[/tex]

Answer:

1820 ways

Step-by-step explanation:

Formula of a combination

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

Here, n = 16 and r = 4.

Solving

  • ¹⁶C₄
  • 16! / 12! 4!
  • 16 x 15 x 14 x 13 x 12! / 12! x 4 x 3 x 2 x 1
  • 16 x 15 x 14 x 13 / 24
  • 2 x 5 x 14 x 13
  • 10 x 182
  • 1820 ways