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When n is large, n! can be approximated by means ofthe expression√2πnnen called Stirling’s formula, where e is the base of naturallogarithms. (A derivation of this formula may be found inthe book by W. Feller cited among the references at theend of this chapter.)(a) Use Stirling’s formula to obtain approximations for10! and 12!, and find the percentage errors of these approximations by comparing them with the exact val-ues given in table Factorials and Binomial Coefficients of “Statistical Tables.”(b) Use Stirling’s formula to obtain an approximation forthe number of 13-card bridge hands that can be dealt withan ordinary deck of 52 playing cards.

When n is large, n! can be approximated by means ofthe expression√2πnnen called Stirling’s formula, where e is the base of naturallogarithms. (A derivation of this formula may be found inthe book by W. Feller cited among the references at theend of this chapter.)(a) Use Stirling’s formula to obtain approximations for10! and 12!, and find the percentage errors of these approximations by comparing them with the exact val-ues given in table Factorials and Binomial Coefficients of “Statistical Tables.”(b) Use Stirling’s formula to obtain an approximation forthe number of 13-card bridge hands that can be dealt withan ordinary deck of 52 playing cards.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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When n is large, n! can be approximated by means of
the expression
√
2πn
n
e
n
called Stirling’s formula, where e is the base of natural
logarithms. (A derivation of this formula may be found in
the book by W. Feller cited among the references at the
end of this chapter.)
(a) Use Stirling’s formula to obtain approximations for
10! and 12!, and find the percentage errors of these
approximations by comparing them with the exact val-
ues given in table Factorials and Binomial Coefficients of
“Statistical Tables.”
(b) Use Stirling’s formula to obtain an approximation for
the number of 13-card bridge hands that can be dealt with
an ordinary deck of 52 playing cards.
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