Question

A lottery game requires that you pick 66 different numbers from 1 to 7575. If you pick all 66 winning​ numbers, you win the jackpot. If you pick 55 of the 66 numbers​ correctly, you win ​$250 comma 000250,000. In how many ways can you pick exactly 55 of the 66 winning numbers without regard to​ order?

Answer 1

1.074×10^12 ways

Explanation:

Number of ways is given by n combination r

n combination r = n!/(n-r)!r!

n = 66, r = 55

66 combination 55 = 66!/(66-55)!55! = 66!/11!55! = (66×65×64×63×62×61×60×59×58×57×56×55!)/(11×10×9×8×7×6×5×4×3×2×1×55!) = (66×65×64×63×62×61×60×59×58×57×56)/(11×10×9×8×7×6×5×4×3×2×1) = 1.074×10^12