d) Let’s let Nk denote the number of ways to climb k stairs in the manner described. (So we’re looking for N10.) Notice that for k ≥ 4 there are 3 “moves” one can do for your first step: you can climb 1,2, or 3 stairs. If you climb 1 stair then there are Nk−1 ways to finish; if you climb 2 stairs there are Nk−2 ways to finish; and if you climb 3 stairs there are Nk−3 ways to finish. Thus:
Nk = Nk−1 + Nk−2 + Nk−3
Well, it’s pretty easy to see that for the k < 4 we have N1 = 1, N2 = 2 and N3 = 4, so using the above we can calculate N10 using
So there are 274 ways to climb the stairs.
c) F (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34....................
The initial values F0=0 and F1=1 are part of the definition of the Fibonacci sequence. They can't be derived, because e.g. you could just as well pick any two numbers and apply the same recursion relation to get a different sequence. They're just the simplest numbers to start with.
b) Candy = 1
ice cream = 2
Let take n = 1 ==> 1candy = 1way
Let take n = 2 ==> 2candy or 1 icecream = 2 ways
Let take n = 3 ==> 3candy or 1candy+1icecreamz = 2ways
Let take n = 4 ==> 4 candy or 2candy+1icecream or 2icecream = 3ways
Let take n = 5 ==> 5C or 3C + 1I or 1C + 2I = 3ways
Let take n = 6 ==> 6C or 4C + 1I or 2C + 2I or 3I = 4ways
Let take n = 7 ==> 7C or 5C + 1I or 3C + 2I or C+3I = 4ways
Let take n = 8 ==> 8C or 6C + 1I or 4C + 2I or 2C + 3I + 4I = 5ways
From the above we can say that the formula is
ways
a) Let Nk be the number of ways to get up k stairs, where you can either take one or two steps at a time. Obviously N(1)=1 because when you have one stair left all you can do is walk up it.
With two stairs left to go, we can go up both stairs at once or we can go up one stair and be on stair 1. So N(2)=1+N(1)=1+1=2
Similarly as above problem
So there are 89 ways to climb the stairs.
If you have any doubts please reply in here i will answer.Please rate the answer.Thank you
Set 5 a. A staircase has 10 steps. You walk up taking one or two at a time. How many ways can you...
Python Programming. There exists a staircase with N steps, and you can climb up either 1 or 2 steps at a time. Given N, write a function that returns the number of unique ways you can climb the staircase. The order of the steps matters. For example, if N is 4, then there are 5 unique ways: 1, 1, 1, 1 2, 1, 1 1, 2, 1 1, 1, 2 2, 2
Suppose we have a staircase with n steps (we start on the ground, so we need n total steps to reach the top). We can take as many steps forward at a time, but we will never step backwards. How many ways are there to reach the top? Give your answer as a function of n. For example, if n=3, then the answer is 4. The four options are the following: (1) take one step, take one step, take one...
Problem 2 a) In how many ways can 6 women and 5 men line up so that no two men are next to one another? b) In how many ways can 7 different pairs of twins line up so that twins must be next to one another? c) In how many ways can 7 women and 10 men sit at a circular table so that no two women are sitting side by side? d) How many strings of length 5...
math a) How many ways you can pick one boy and one girl from 6 boys and 7 girls? b) How many 4 digit numbers greater than 3000 can be formed? c) How many ways can 3 books can be selected out of 10 books? d) How many ways can 3 books can be arranged out of 10 books? e) How many 2 letter words can we make with the letters in the word QUIZ?
1. How many different ways can you have r numbers 1 sum up to a number n? These are called compositions of a number n and it is easy to calculate from our understanding of binomial coefficients. So the number of compositions of 4 into 3 parts will be 1+1+2, 1+2+1, and 2+1+1. Note how we think of 1+1+2 and 1+2+1 as different-because in the first case, the first number is 1, second is 1 and third is 2, while...
you roll a fair die 4 times how many ways can you get at least one 3? how many ways can you get at most two 3's?
please illustrate each stepbof the solution so I can understand thank you 4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint the numbered vertices, if two colors (red and blue) are available? (b) How many ways, if additionally we want that at most two numbered vertices are painted red? 4) Given the diagram 2 7 3 6 4 (a) Up to symmetries, in how many ways can we paint...
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...
5) (a) In how many ways can we distribute 10 different chocolates to 4 children so that every child gets at least one chocolate? (b) In how many ways can we distribute 5 different chocolates to 9 children so that every child gets at most one chocolate? 5) (a) In how many ways can we distribute 10 different chocolates to 4 children so that every child gets at least one chocolate? (b) In how many ways can we distribute 5...
A 10-pack of batteries has two defective batteries. In how many ways can one select three of these batteries and get a. Neither of the defective batteries? b. One of the defective batteries? c. Both of the defective batteries?