In a certain state, people can choose between two lotteries, A and B. To win Lottery A, one must correctly select five numbers from 1 to 40 (repeats not allowed and order not important)

GRE Quant Problem Solving
1

Prob
Prob1704×1063 120 KB

I’m stuck on this question, does anyone know how to solve? Thanks!

2

Total sets of 5 numbers they can choose from 40 (repeats not allowed, order unimportant) = \frac{40!}{35! * 5!} = \frac{40 * 39 * 38 * 37 * 36}{5 * 4 * 3 * 2 * 1} = 658008

Total arrangements of 5 numbers they can choose from 11 (repeats allowed, order important) = 11 * 11 * 11 * 11 * 11 = 161051

Total number of balls to select from = 4

P(A) = \frac{1}{658008}
P(B) = \frac{1}{161051 * 4} = \frac{1}{644204}
P(B) > P(A)
Ans. B

3

Thanks so much!