Exercise 8 At a gathering there are n chairs and some collection of people (including possibly none) will sit in the seats but there will always be at least one empty chair between any two people. Let an be the number of antisocial ways to seat some number of people in these n seats as described. Compute an and construct all possible arrangements for all values up to n 4. Find and prove the correctness of a recursive formula for an.

Q: How many 3-digit numbers can we make using the digits 2, 3, 4, 5, and 6 without repetitions?

A: here available digit 2,3,4,5 and 6 total 5 digits available

Q: Supposed repetitions are not allowed. Find the number n of three-digit even numbers that can be…

A:

Q: How many Combinations 3-letter Possible from letters A, E, I, O, and 4?

A: Here the given letters are ,      A,E,I,O,U  So, total number of letters , n=5 Using formula ,…

Q: 4, and 6 if no digit is repeated in any number? a. b. repetitions are allowed?

A:

Q: If a license number is selected randomly, what is the probability that yours is the one selected?

A: 3 places to be filled with 10 choices for each place: 10*10*10= 10³ = 1000

Q: How many three-letter "words" (some may be nonsense words) can be made from 4 letters "FGHI" if…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: How many different four letter secret codes can be formed if the first letter must be an S or a T ?

A: The experiment is to form four-letter secret codes. The condition is the first letter must be an S…

Q: How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if the number is odd and…

A: numbers: {3,2,7,6,0,4,9} make 4 digit numbers  no repeatation odd numbers: last digit must be odd.…

Q: How many ways to arrange 7 books on the shelf exist if two definite books are not placed together?

A:

Q: What is the sum of the 2nd and 16th Fibonacci numbers?

A: Fibonacci sequence is given by recurrence relation  Fn=Fn-1+Fn-2, F1=1, F2=1

Q: How many three – digit numbers greater than 300 can be formed with the digits 1, 2, 3, 4 and 5 if no…

A: According to the provided information, The digits are 1, 2, 3, 4, 5 and no repetitions are allowed?…

Q: how many 3-digit number we can form using 10 digits (0,1,2,3.......,8) if no repetition is allowed

A: The first digit have 9 choices (digits 1 -9) as zero cannot be the first digit.There will be 9…

Q: How many seven-digit numbers can be made from the digits 1 to 9 if repetition is allowed?

A: Given that  To find the number of ways of 7 digit number can be made from the 1 to 9

Q: How many four-digit numbers can be formed from the digit 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 if each digit…

A: here available digits are 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 so total 10 digits available here each digit…

Q: Question 3 The next number in the sequence 0,3,8, 15, 14, ... is

A: Given sequence is 0,3,8,15,14,...

Q: In how many ways can 3 letters be put in five boxes

A: Number of boxes available = 5 Number of letters = 3 Hence, the number of ways in x letters can be…

Q: 1. Consider a 4 digit number abcd and show that abcd−(a+b+c+d) is always divisible by 9. (Ex 1234 −…

A: Since it is a multiple question. As per our company guidelines, we have to solve the first question.…

Q: How many ways are there to rearrange the letters in the word "TAKUT" so that the two Ts are not next…

A:

Q: How many four-digit numbers can be made from the digits 1 to 6 if repetition is allowed?

A: Number of four digit can be made from digits  1 to 6 :