How many different groups of 5 problems can be chosen from the 14 problems?

A scientist investigated the effect of​ cross-fertilization on the heights of plants. In one​ study, the scientist planted 15pairs of a species of plant. Each pair consisted of one​ cross-fertilized plant and one​ self-fertilized plant grown in the same pot. The table available below gives the height​ differences, in eighths of an​ inch, for the 15 pairs. Each difference is obtained by subtracting the height of the​ self-fertilized plant from that of the​ cross-fertilized plant. Use the paired​ t-interval procedure to determine a 99​% confidence interval for the difference between the mean heights of​ cross-fertilized and​ self-fertilized plants. Interpret the result.​ (Note: d=19.00 and sd=35.50​.)       The 99​%confidence interval is from ____ eighths of an inch to_____ eighths of an inch. ​(Round to two decimal places as needed. Use ascending​ order.)   Which statement below best interprets the confidence​ interval? A. There is 99​%confidence that the difference between the…

Natasha and Rodrigo are in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that either Natasha and Rodrigo are both selected or Natasha and Rodrigo are both not selected?  Show all work.   You do not need to multiply out the final answer.

There were 127 pears and oranges in a box at first. 2/5 of the pears and 2/3 of the oranges were given away. In the end, there were a total of 65 pears and oranges left. How many more pears than oranges were in the box at first?