Mrs. Brown has 17 children in her first-grade class, and Mr. Lopez has 20 children in his second-grade class. The principal has been asked to select 1 student from one of the classes to appear at a PTA meeting. How many ways can the selection be made?
A speaker has a collection of 62 jokes. He uses 3 jokes in each speech.
How many speeches can he give without using a joke twice? (Round your answer down to the nearest whole number.)
To find the number of ways the principal can select one student from either Mrs. Brown's class or Mr. Lopez's class, we can use the concept of combinations.
The number of ways to select one student from Mrs. Brown's class is denoted as "17 choose 1" or "C(17, 1)". This can be calculated using the formula for combinations:
C(n, r) = n! / (r! * (n - r)!),
where n is the total number of items to choose from, and r is the number of items to select. In this case, n = 17 (number of children in Mrs. Brown's class) and r = 1 (the principal has to select 1 student).
Plugging the values into the formula:
C(17, 1) = 17! / (1! * (17 - 1)!) = 17! / (1! * 16!) = 17.
So, there are 17 ways to select one student from Mrs. Brown's class.
Similarly, the number of ways to select one student from Mr. Lopez's class is "20 choose 1" or "C(20, 1)". Applying the same formula:
C(20, 1) = 20! / (1! * (20 - 1)!) = 20! / (1! * 19!) = 20.
Therefore, there are 20 ways to select one student from Mr. Lopez's class.
To find the total number of ways the selection can be made, we can add the number of ways from each class:
17 (from Mrs. Brown's class) + 20 (from Mr. Lopez's class) = 37.
Hence, there are a total of 37 ways the principal can select one student from either class to appear at the PTA meeting.