A student is required to work exactly 9 problems from a 14-problem exam and must work exactly 3 of the first 5 problems. In how many ways can the 9 problems be chosen?
+23254 This is a combinations problem.
The number of ways to choose 3 of the first 5 problems is: 5C3 = 10.
There are 9 problems remaining (14 - 5 = 9) and six more problems must be chosen (9 - 3 = 6); the number of ways to choose 6 of these 9 problems is: 9C6 = 84.
Since both of these conditions must be met, multiply these numbers together: 10 x 84 = 840.
+23254 This is a combinations problem.
The number of ways to choose 3 of the first 5 problems is: 5C3 = 10.
There are 9 problems remaining (14 - 5 = 9) and six more problems must be chosen (9 - 3 = 6); the number of ways to choose 6 of these 9 problems is: 9C6 = 84.
Since both of these conditions must be met, multiply these numbers together: 10 x 84 = 840.
