Determine the number of permutations of 10 objects taken six at a time. Determine the number of combinations of 10 objects taken six at a time. That is, determine Suppose there is a lottery in which four balls are drawn from an urn containing 10 balls. A winning ticket must show the balls in the order in which they are drawn. How many distinguishable tickets exist? Suppose there is a lottery in which four balls are drawn from a bin containing 10 balls. A winning ticket must merely show the correct balls without regard for the order in which they are drawn. How many distinguishable tickets exist? Use mathematical induction to prove the Binomial theorem, given in Section A.7. Show the validity of the following identity. 2n 2 +n² Assume that we have ki objects of the first kind, k₂ objects of the second + km = 12. kind,. and km objects of the mth kind, where ki + k + Show that the number of distinguishable permutations of these n objects is equal to n! (k₂!) (k₂!) (km!)

Determine the number of permutations of 10 objects taken six at a time. Determine the number of combinations of 10 objects taken six at a time. That is, determine Suppose there is a lottery in which four balls are drawn from an urn containing 10 balls. A winning ticket must show the balls in the order in which they are drawn. How many distinguishable tickets exist? Suppose there is a lottery in which four balls are drawn from a bin containing 10 balls. A winning ticket must merely show the correct balls without regard for the order in which they are drawn. How many distinguishable tickets exist? Use mathematical induction to prove the Binomial theorem, given in Section A.7. Show the validity of the following identity. 2n 2 +n² Assume that we have ki objects of the first kind, k₂ objects of the second + km = 12. kind,. and km objects of the mth kind, where ki + k + Show that the number of distinguishable permutations of these n objects is equal to n! (k₂!) (k₂!) (km!)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...

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Concept explainers

Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.

Question

Determine the number of permutations of 10 objects taken six at a time.
9. Determine the number of combinations of 10 objects taken six at a time. That
is, determine
10
6
0. Suppose there is a lottery in which four balls are drawn from an urn containing
10 balls. A winning ticket must show the balls in the order in which they are
drawn. How many distinguishable tickets exist?
Suppose there is a lottery in which four balls are drawn from a bin containing
10 balls. A winning ticket must merely show the correct balls without regard.
for the order in which they are drawn. How many distinguishable tickets
exist?
Use mathematical induction to prove the Binomial theorem, given in
Section A.7.
Show the validity of the following identity.
(²) -- () --
2
+n²
1. Assume that we have ki objects of the first kind, k₂ objects of the second
kind,..., and km objects of the mth kind, where k₁+k2 + ... + km = n.
Show that the number of distinguishable permutations of these n objects is
equal to
n!
(ki!) (k₂!) (km!)

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