Unformatted text preview: screte
Mathematics and Statistics. We introduce these concepts here because this is how the factorials
make their way into the Binomial Theorem, as our next deﬁnition indicates.
Definition 9.5. Binomial Coeﬃcients: Given two whole numbers n and j with n ≥ j , the
n
binomial coeﬃcient
(read, n choose j ) is the whole number given by
j
n
n!
=
j
j !(n − j )!
The name ‘binomial coeﬃcient’ will be justiﬁed shortly. For now, we can physically interpret
n
j as the number of ways to select j items from n items where the order of the items selected is
unimportant. For example, suppose you won two free tickets to a special screening of the latest
Hollywood blockbuster and have ﬁve good friends each of whom would love to accompany you to
the movies. There are 5 ways to choose who goes with you. Applying Deﬁnition 9.5, we get
2
5
2 = 5!
5!
5·4
=
=
= 10
2!(5 − 2)!
2!3!
2 So there are 10 diﬀerent ways to distribute those two tickets among ﬁve friends. (Some will see it
as 10 ways t...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details