### Problem Set on Combinatorics**Instructions:** Answer the questions below. If necessary, consult a list of formulas.---**Question (a):** A certain committee consists of 16 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.**Question (b):**An experiment involves 31 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible?

Answered: Answer the questions below. (If…

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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Step 1: Determine permutation and combination

In order to select $r$ objects from $n$ total available objects, where the order of the selection (or rank) is not considered, the concept of combination is used. It is formulated as: $^{n} C_{r} = \frac{n!}{r! (n - r)!}$ ; $n \geq r$ .

Whereas, in order to select $r$ objects from $n$ total available objects, where the order of the selection (or rank) is considered, the concept of permutation is used. It is formulated as: $^{n} P_{r} = \frac{n!}{(n - r)!}$ ; $n \geq r$ .