Determine the number of ways a computer can randomly generate two distinct integers whose sum is 20 from 1 through 25 in increasing order.
A)7
B)5
C)11
D)13
E)9

Question

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 20 from 1 through 25 in increasing order. ​
A)7
B)5
C)11
D)13
E)9

Quizplus · Accepted Answer

To find two distinct integers whose sum is 20, we can start with the smallest number, 1. The pair would then be (1, 19). We continue this process until we reach a pair where both numbers are within the range of 1 through 25 and in increasing order. The pairs are (1, 19), (2, 18), (3, 17), (4, 16), (5, 15), (6, 14), (7, 13), (8, 12), and (9, 11). After (9, 11), the next pair would be (10, 10), which is not considered because the problem specifies the integers must be distinct. Therefore, there are 9 valid pairs.

Determine the Number of Ways a Computer Can Randomly Generate