Find a rec. relation for an,k, the number of ways to order n doughnuts from k...
Find a rec. relation for an,k, the number of ways to order n doughnuts from k different types of doughnuts if two or four or six doughnuts must be chosen of each type.
Answer is an,k = an-2,k-1+an-4,k-1+ an-6,k-1., please explain how to geit it, thanks.
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Find a rec. relation for an,k, the number of ways to order n
doughnuts from k...
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 21 subsequence. b) Find a recurrence relation for an, the number of sequen...
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 21 subsequence. b) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 44 subsequence. Answer is a) an = an-1+ an-4 + an-2 - an-3, b) an = an-1 + an-2 + an-5 + an-6, please explain how to get it,...
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's...
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 21 subsequence. b) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 44 subsequence. Answer is a) an = an-1+ an-4 + an-2 - an-3, b) an = an-1 + an-2 + an-5 + an-6, please explain how to get it,...
06. Do any two of the following three parts Q6(a). Solve the following recurrence relation; Q6(b). Find a recurrence relation for an, which is the number of n-digit binary sequences with no pa...
06. Do any two of the following three parts Q6(a). Solve the following recurrence relation; Q6(b). Find a recurrence relation for an, which is the number of n-digit binary sequences with no pair of consecutive 1s. Explain your work. Q6(c) Solve the following problem using the Inclusion-Exclusion formula. How many ways are there to roll 8 distinct dice so that all the six faces appear? Hint: Use N(A'n n. NU)-S-,-1)' )-S-S2+S-(-1)Sn U- All possible rolls of 8 dice, Aj-Roll of...
need steps A small post office has only 4-cent, 6-cent and 10-cent stamps Find a recurrence relation for the number...
need steps
A small post office has only 4-cent, 6-cent and 10-cent stamps Find a recurrence relation for the number of ways to form postage of n cents if the order of the stamps matters, i.e.. different orderings add to the count a. b. How many ways are there to form postage of 20 cents? Fill in the following chart 10 14 6 8 16 20 0 40 18 Extra Credit:
A small post office has only 4-cent, 6-cent and...
Find out the number of ways of dividing n different chocolates to 3 children such that...
Find out the number of ways of dividing n different chocolates to 3 children such that the each of them gets a, b and c chocolates respectively by coming up with a k-to-1 function between the set of all permutations of the n chocolates and the set of all distinct ways of dividing the chocolates among the 3 children.
14. Find a recurrence relation for the number of permutations of the integers (1,2,3,...,n that h...
How to solve these problem, I need detailed answer process.
14. Find a recurrence relation for the number of permutations of the integers (1,2,3,...,n that have no integer more than one place removed from its natural position in the order
14. Find a recurrence relation for the number of permutations of the integers (1,2,3,...,n that have no integer more than one place removed from its natural position in the order
How many ways can n identical balls be distributed into k bins such that each bin...
How many ways can n identical balls be distributed into k bins such that each bin contains at least two balls? Assume that n ≥ 2k. Please type your answer or use neat handwriting.
Problem1 Answer the following questions with a number or a simple formula involving factorials an...
6.042 - 1
Problem1 Answer the following questions with a number or a simple formula involving factorials and binomial coef. ficients. Briefly explain your answers. (a) How many ways are there to order the 26 letters of the alphabet so that no two of the vowels a, e, i, o, u appear consecutively and the last letter in the ordering is not a vowel? Hint: Every vowel appears to the left of a consonant ters of the alphabet so that...
1. In how many ways can four aces be drawn from a deck of cards? (Order...
1. In how many ways can four aces be drawn from a deck of cards? (Order is not important.) 2. If a family has six children, in how many ways could the parents have four boys and two girls? 3. Decide whether you would use a permutation, a combination, or neither. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question. 4. A club with 23 members is to select a committee of...
15to25 15.How many ways are there to seat ten people around a circular table where two seatings are considered the s...
15to25
15.How many ways are there to seat ten people around a circular table where two seatings are considered the same when every one has the same immediate left and immediate right neighbor? 16.In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if a) the bride must be next to the groom? b) the bride is not next to the groom? 17.How many bit strings of length seven...
06. Do any two of the following three parts Q6(a). Solve the following recurrence relation; Q6(b). Find a recurrence relation for an, which is the number of n-digit binary sequences with no pair of consecutive 1s. Explain your work. Q6(c) Solve the following problem using the Inclusion-Exclusion formula. How many ways are there to roll 8 distinct dice so that all the six faces appear? Hint: Use N(A'n n. NU)-S-,-1)' )-S-S2+S-(-1)Sn U- All possible rolls of 8 dice, Aj-Roll of...
need steps
A small post office has only 4-cent, 6-cent and 10-cent stamps Find a recurrence relation for the number of ways to form postage of n cents if the order of the stamps matters, i.e.. different orderings add to the count a. b. How many ways are there to form postage of 20 cents? Fill in the following chart 10 14 6 8 16 20 0 40 18 Extra Credit:
A small post office has only 4-cent, 6-cent and...
Find out the number of ways of dividing n different chocolates to 3 children such that the each of them gets a, b and c chocolates respectively by coming up with a k-to-1 function between the set of all permutations of the n chocolates and the set of all distinct ways of dividing the chocolates among the 3 children.
How to solve these problem, I need detailed answer process.
14. Find a recurrence relation for the number of permutations of the integers (1,2,3,...,n that have no integer more than one place removed from its natural position in the order
14. Find a recurrence relation for the number of permutations of the integers (1,2,3,...,n that have no integer more than one place removed from its natural position in the order
6.042 - 1
Problem1 Answer the following questions with a number or a simple formula involving factorials and binomial coef. ficients. Briefly explain your answers. (a) How many ways are there to order the 26 letters of the alphabet so that no two of the vowels a, e, i, o, u appear consecutively and the last letter in the ordering is not a vowel? Hint: Every vowel appears to the left of a consonant ters of the alphabet so that...
15to25
15.How many ways are there to seat ten people around a circular table where two seatings are considered the same when every one has the same immediate left and immediate right neighbor? 16.In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if a) the bride must be next to the groom? b) the bride is not next to the groom? 17.How many bit strings of length seven...
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