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A group of high school students is preparing to compete with groups from other schools on a TV show in which questions.
How many different meals are possible if the cold appetizer and dessert are served with all meals and the entries are served in the order of selection?
The name of a variable in the C programming language is a string that can contain uppercase letters, lowercase letters, digits, or underscores.
I want to create two play lists on my MP3 player from my collection of 500 songs. One playlist is titled "Exercise" for listening in the gym.
How many numbers are there in {1, 2, . . . . , 1000} which have at least one digit equal to 3?
There are 10 workers and 2 administrators in a company meeting room. Two people will be selected at random without replacement.
How many ways are there to deal hands of seven cards to each of five players from a standard deck of 52 cards?
Of the 28 members, 15 are men and the rest are women. How many ways can the 6 member committee can be selected if there are to be 4 men and 2 women.
In 2 rows, where 7 of the vehicles are trucks to be arranged in one row, and the other 11 vehicles are cars, to be arranged in another row?
Cardinality of sets and how cardinality relates to the number of subsets of a set.
How many positive integers between 1000 and 9999 inclusive are divisible by 9?
How many such sets of committees are possible if there is no restriction on the number of committees on which a person may serve?
Sarah, Jolly and Betty are female triplets. They and their 10 cousins are posing for a series of photographs. One pose involves all 13 children.
How many ways are there to select a committee of 5 members if at least 1 man and 1 woman must be on the committee?
Find an upper bound for the number of possible states in the game of chess, assuming that draw-by-repetition is enforced if the same position.
The National association of college and university business officers researched the change in university and college endowments from 2007 to 2008.
A certain city has experienced a relatively rapid increase in traffic congestion in recent times. The mayor has decided that it's time.
Show that every cyclic group Cn of order n is abelian. (Moreover, show that if G is a group, so is GxG)
If G is any group, define $:G->G by $(g) = g^-1. Show that G is abelian if an only if $ is a homomorphism.
If K is a normal subgroup of G has index m, show that g^m belongs to K for all g belonging to G.
Elements of Sn can be written in an alternative form, called cycle notation. Starting with 1, we see that s(1) = 3 s(4) = 1, back to the start.
Prove that if G1 and G2 are abelian groups, then the direct product G1 x G2 is abelian.
Let G sub1 and G sub 2 be groups, with subgroups H sub 1 and H sub 2, respectivetly. Show that {(x sub 1, x sub 2).
Let p be a prime number and G a group of order p2 with identity element e. let U ? G and U ? {e} be a subgroup of G. prove that U is cyclic.
Show that if a elements in G where G is a finite group with the identity, e, then there exist n elements in Z+ such that a n =e