The numbers on lottery tickets are formed by combinations of certain numbers previously agreed upon; as from 1 to 60, 1 to 75, 1 to 78, &c., &c.
Combination consists in taking a less number of things out of a greater, without any regard to the order in which they stand; no two combinations having the same quantities or numbers.
_Problem._--To find the number of combinations which can be taken from any given number of things, all different from each other, taking a given number at a time.
_Rule._--Take a series of numbers, the first term of which is equal to the number of things out of which the combinations are to be made, and decreasing by 1, till the number of terms is equal to the number of things to be taken at a time, and the product of all the terms.
Then take the natural series 1, 2, 3, &c., up to the number of things to be taken at a time, and find the product of all the terms of this series.
Divide the former product by the latter, and the quotient will be the answer.
How many combinations of 3 numbers can be taken out of 78 numbers?
78×77×76 = 456456 and 1×2×3 = 6 6)456456 ------ 76076 Answer.
How many combinations of 3 numbers can be taken out of 70 numbers?
70×69×68 = 328440 and 1×2×3 = 6 6)328440 ------ 54740 Answer.
How many combinations of 3 numbers can be taken out of 60 numbers?
60×59×58 = 205320 and 1×2×3 = 6 6)205320 ------ 34220 Answer.
How many combinations of 3 numbers can be taken out of 40 numbers?
40×39×38 = 59280 and 1×2×3 = 6 6)59280 ----- 9880 Answer.
We have sufficient experience in lottery gambling to assure the community that their whole system is as foul as highway robbery. We purchased a wheel from one of the fraternity in Washington City, and drew in Philadelphia three times, then carried it to Washington, and there demonstrated to the satisfaction of those who witnessed our drawing, that what we asserted was true to the letter. We copy the notices of the American Courier, one of the first papers of our country in the cause of humanity, and ever ready to diffuse that which will promote the happiness and welfare of mankind.
"On Saturday night, drew the prize of fifty dollars for the proprietor, he having declared to the audience the intention of giving them blanks, which he did to the satisfaction of the judges. We have the best authority for stating the belief that his expositions will prove not only interesting, but highly beneficial, in opening the eyes of thousands to the frauds practised in the shape of fairness by the lottery managers."