Match each problem to its solution formula by dragging a label from below and placing it next to the problem. • How many ways can we hire people from a pool of k candidates for n different positions? • How many ways can a hiring committee consisting of k members be formed from n available colleagues in a department? • A council consisting of n representatives is to be chosen from a community that is comprised of k ethnic groups. How many ethnic compositions can the council take on?

Match each problem to its solution formula by dragging a label from below and placing it next to the problem. • How many ways can we hire people from a pool of k candidates for n different positions? • How many ways can a hiring committee consisting of k members be formed from n available colleagues in a department? • A council consisting of n representatives is to be chosen from a community that is comprised of k ethnic groups. How many ethnic compositions can the council take on?

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Description: Match each problem to its solution formula by dragging a label from below and placing it next to the problem.• How many ways can we hire people from a pool of k candidates for n different positions?• How many ways can a hiring committee consisting o

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

Match each problem to its solution formula by dragging a label from below and placing it next to the problem.
• How many ways can we hire people from a pool of k candidates for n different positions?
• How many ways can a hiring committee consisting of k members be formed from n available colleagues in a department?
• A council consisting of n representatives is to be chosen from a community that is comprised of k ethnic groups. How many ethnic compositions can the council take on?
How many k-character passwords can be created using a set of n characters?
Labels:
n to the power of k
C(n+k-1,k)
P(k,n)
C(k,n)
k to the power of n
C(n,k)
P(n,k)
C(n+k-1,n)

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