Question

From a club of 16 ​people, in how many ways can a group of four members be selected to attend a​ conference?

Answer 1

1820 ways

Step-by-step explanation:

Formula of a combination

• 
  `^(n)C_(r) = (n!)/((n-r)!r!)`

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

Answer 2

1820 ways

Step-by-step explanation:

Use combination method. where order does not matter.

`\sf _n C_r=(n !)/(r ! (n-r) !)` : combination formula

Solve:

`\sf \bold{\cdot}} \ _(16) C_4`

`\sf \bold{ \cdot} \ (16!)/(4!(16-4)!)`

`\sf \bold{ \cdot} \ (16!)/(4! \ x \ 12!)`

`\sf \bold{ \cdot} \ 1820`