1. How many different ways can you have r numbers 1 sum up to a number...
How many different three-digit numbers can be written using the digits 4, 5, 6, and 7? Use each digit only once in a number. Is the answer---24 different 3-digit numbers? I did this the long way--Is there a short equation to use for this? Thank you!You have four digits: The first choice can be any of the 4, there are four ways to get it. The second choice can be any of three, there are three ways.. and so on....
What numbers can be expressed as an alternating-sum of an increasing sequence ofpowers of 2 ?To form such a sum, choose a subset of the sequence 1, 2, 4, 8, 16, 32, 64, . . . (these arethe powers of 2). List the numbers in that subset in increasing order (no repetitionsallowed), and combine them with alternating plus and minus signs. For example,1 = – 1 + 2; 2 = – 2 + 4; 3 = 1 – 2 +...
Here is the question: In how many ways can John, Todd, Lisa, and Marie line up so that they alternate gender? Here is the solution that I came up with (Choices for gender)*(Number of ways to arrange the genders) There two choices for gender: either a girl or a boy. For the first position you can choose two boys, in the second you can choose two girls, in the third you can choose one boy, and in the fourth you...
Set 5 a. A staircase has 10 steps. You walk up taking one or two at a time. How many ways can you go up? We have n dollars to spend. Every day we either buy a candy for 1 dollar, or an ice cream for 2 dollars. In how many ways can we spend the money? Explain for n-5, and then conjecture for n dollars. Prove your conjecture. Define Fibonacci numbers completely. Why do you need two initial values?...
How many different integers can be expressed as the sum of three different numbers in the set (1,2,3,4,5,6,7)?Can anyone explain this one to me???Thank you!
use python: Write a program that reads in X whole numbers and outputs (1) the sum of all positive numbers, (2) the sum of all negative numbers, and (3) the sum of all positive and negative numbers. The user can enter the X numbers in any different order every time, and can repeat the program if desired. Sample Run How many numbers would you like to enter? 4 Please enter number 1: 3 Please enter number 2: -4 Please enter...
2. How many ways can you pick a license plate with 3 letters, then 4 numbers? 3. How many ways can you list 4 numbers out of a list consisting of 7 numbers without repetition?
guided exercise 11, pg. 225 a. evaluate 31. 31 = 3, 2, 1 = 6 b. in how many different ways can three objects be arranged in order? how many choices do you have for the first position? for the second nd position? for the third position? you have three choices for the first pos. two for the second pos. and one for the third pos. by the multiplication you have (3) (2) (1) = 31 = 6 arrangements
1. How many ways can a group of six boys and sik girls be seated in a row of twelve seats if boys and girls must alternate in the row? ways 2. How many ways can 4 different contracts be distributed amongst 15 different firms, if any one firm can be awarded multiple contracts? ays 3. How many four-digit numbers may be formed using elements from the set (1, 2, 3,4, 5,6,7,8,9) if no element may be used more than...