Question

In how many ways can one select a panel of 15 from 34 people.

Answer 1

1,855,967,520

Explanation:

I guess the sequence inside the picked panel of 15 is not important.

then we have combinations :

34! / (15! × (34-15)!) = 34! / (15! × 19!)

= 34×33×32×31×30×29×28×27×26×25×24×23×22×21×20 / 15×14×13×12×11×10×9×8×7×6×5×4×3×2×1 =

= 34×33×32×31×2×29×2×27×2×25×2×23×2×21×2 /

9×8×7×6×5×4×3×2×1 =

= 34×33×4×31×2×29×2×3×2×5×2×23×2×3×2 /

6×4×3×2×1 =

= 34×11×1×31×1×29×1×1×2×5×2×23×2×3×2 =

= 34×31×29×23×11×5×3×2⁴ =

= 34×31×29×23×16×11×5×3 = 1,855,967,520