GROUP #1: Fundamental Principle of Counting1 How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that(i)repetition of the digits is allowed.(ii)repetition of the digits is not allowed.repeated?2. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can bePermutcan be repeated?3. How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter4. How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number startswith 67 and no digit appears more than once?5. A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?6. Given 5 flags of different colors, how many different signals can be generated if each signal requiresthe use of 2 flags, one below the other?GROUP #2: Permutations1. How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?How many 4-digit numbers are there with no digit repeated?2.3. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit isrepeated?4.Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit isrepeated. How many of these will be even?5. From a committee of 8 persons, in how many ways can we choose a chairman and a vicechairman assuming one person cannot hold more than one position?6. How many words, with or without meaning, can be formed using all the letters of the wordEQUATION, using each letter exactly once?7. How many words, with or without meaning can be made from the letters of the word MONDAY,assuming that no letter is repeated, if :(i)(ii)4 letters are used at a time, (ii) all letters are used at a time,all letters are used but first letter is a vowel?9. In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not cometogether?10. In how many ways can the letters of the word PERMUTATIONS be arranged if the(iii)words start with P and end with S, (ii) vowels are all together,(iv)there are always 4 letters between P and S?

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Answered: GROUP #1: Fundamental Principle of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The integers from 1 to 7 are written in order clockwise around a circle. I start with a counter on number 1 and repeatedly roll a standard six-sided fair die. If the die shows 1 then I move the counter to the next number clockwise around the circle; if the die shows 2 or 3 then I move the counter to the next number anticlockwise around the circle; if the die shows 4, 5 or 6 then I do not move the counter. (i) Describe how to model this process as a discrete-time Markov chain. Write the transition matrix (ii) Explain why the Markov property is satisfied and give an example of how you could make a small modification after which the process would be a discrete-time Markov chain which is not homogeneous.
Permutations Use the permutations to solve the given problem. Explain your answer. Show your solution. 1) There are 6 plates numbered 4, 5, 6, 7, 8, and 9. a) If you choose 3 plates out of 6 and arrange them in a row, how many three-digit numbers can be formed? b) If you choose 3 plates out of 6 and arrange them in a row, how many different three-digit odd numbers can be formed? c) you choose 3 plates out of 6 and arrange them in a row, how many different three-digit numbers larger than 700 can be formed? Show your solution.
For all natural numbers, P ( n , n ) = n ! True False
52. Shaking Hands in a Group A group of six strangers sat in a circle, and each one got acquainted only with the person to the left and the person to the right. Then all six people stood up and each one shook hands (once) with each of the others who was still a stranger. How many handshakes occurred?
موضوع الدرس Date: الموافق 1-Use mathematical Induction to Dove that 1°+ 23 +3°+.n3_n2 (n+1)2/4 for all positive integers
Until recently, all area codes had a 0 or a 1 as the middle digit and the first digit could not be 0 or 1. Complete parts (a) and (b) below. (a) How many area codes were possible with this arrangement? How many telephone numbers does the current 8-digit sequence permit per area code? (The first two digits that follow the area code cannot start with 0 or 1 or 2. Assume that there are no other restrictions.) ch There are (Type a whole number.) area codes possible. The current 8-digit sequence will permit (Type a whole number.) (b) The actual number of area codes under the previous system is 152. What is the most likely reason for this. discrepancy between this number and your answer in part a? OA. The actual number of area codes is different from the answer to part a because in part (a) only an estimate of the number of area codes was calculated. The actual number of possible area codes is 152. OB. The actual number of area codes is different from the answer to part a because the answer…
= The Fibonacci numbers are a sequence numbers defined by F₁ = 1, F₂ = Fn = Fn-1 + Fn-2 for n ≥ 3. 1, and
Three adults and five children are seated randomly in a row, then how many ways can this be done?
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A classroom has 20 seats and 18 students. (a) How many different ways are there to select any 2seats from the 20 available? (b) How many ways are there for the 18 students to occupy the 18seats that remain after 2 are selected and set aside? (c) How many total ways are there for the 20students to occupy the 18 seats?

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GROUP #1: Fundamental Principle of Counting 1 How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed. (ii) repetition of the digits is not allowed.