1. Let A be a finite set of cardinality n, where n E N, and let k be a non-negative integer. (a) How many ordered selections of k elements from A are there if (i) we allow repetition? (ii) we do not allow repetition? (b) Give the definition of the binomial coefficient ("). (c) If 0 < k < n, prove the formula (:) n(n – 1) - - (n – k +1) k! (d) A class contains 10 students, 6 boys and 4 girls. We need to pick 3 students to represent the class - and we must pick at least one boy and at least one girl. How many ways are there to do this? Explain your answer carefully.

1. Let A be a finite set of cardinality n, where n E N, and let k be a non-negative integer. (a) How many ordered selections of k elements from A are there if (i) we allow repetition? (ii) we do not allow repetition? (b) Give the definition of the binomial coefficient ("). (c) If 0 < k < n, prove the formula (:) n(n – 1) - - (n – k +1) k! (d) A class contains 10 students, 6 boys and 4 girls. We need to pick 3 students to represent the class - and we must pick at least one boy and at least one girl. How many ways are there to do this? Explain your answer carefully.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

1. Let A be a finite set of cardinality n, where n e N, and let k be a non-negative integer.
(a) How many ordered selections of k elements from A are there if
(i) we allow repetition?
(ii) we do not allow repetition?
(b) Give the definition of the binomial coefficient ().
(c) If 0 <k < n, prove the formula
n(n – 1)..- (n – k+1)
k!
(d) A class contains 10 students, 6 boys and 4 girls. We need to pick 3 students to represent
the class – and we must pick at least one boy and at least one girl. How many ways are
there to do this? Explain your answer carefully.

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