Pre Calculus

Question

How many winning lottery numbers are possible of a pick 5 where you must match all five numbers from 52 balls?

a) 2,598,960
b) 6.7 × 1065
c) 311,875,200
d) 120

Answer 1

This is picking 5 out of 52 balls without replacement.

So it is 52 * 51 * 50 * 49 * 38 = 311,875,200

So the answer is c) 311,875,200

Answer 2

you want to think of this as a combination problem, so you're trying to find

C(52, 5) = 52! / 5!(52 - 5)! = 52! / 5!47! = 2,598,960

meaning that the number of winning lottery combinations is 2,598,960

Answer 3

Lottery games are combinations, not permutations. You just need to get the 5 numbers, no matter which order they come up. (like Powerball) Use the formula n!/r!(n-r)! where n=52 and r=5.

52!/(5!)(47!)

(52*51*50*49*48)/(5*4*3*2*1)

after simplifying you get 2,598,960 which is a)

1/311,875,200 is simply just too high of a probability

Answer 4

The answer to this would be C because if you have 5 picks with no replacement then your first event would have 52 possibilities, you second would have 51, your third 50, your fourth 49, and your fifth 48. In multiplying all these possibilities together you get 311,875,200