As a trial for one year, 104 Grade 12 students at a particular high school were required to take at least one of physics, chemistry, or biology.  37 students took physics.  62 students took chemistry.  68 students took biology.  15 students took physics and chemistry only.  3 students took physics and biology only.  21 students took chemistry and biology only. Represent this situation accurately with a Venn diagram: P is physics, C is chemistry, and B is biology.   a) How many students took all three courses?  b) How many students took only one of physics, chemistry, or biology?  There were ___________ students that took only one of physics, chemistry or biology.

Last year a group of 48 students enrolled in Mathematic, French, and Physics. Some students were more successful than others:   –32 passed French, 27 passed Physics, and 33 passed Mathematics;   –26 passed French and Mathematics, 26 passed Physics and Mathematics, and 21 passed French and Physics;   –21 passed French, Mathematics, and Physics. How many students passed one or more of the subject?   Please write clearly thank you.

A cell phone company offers 19 different voice packages and 19 different data packages. Of those, 6 packages include both voice and data. How many ways are there to choose either voice or data, but not both?

If a bag contains 4 blue marbles 6 red marbles and 9 green marbles then the number of ways that 3 marbles of the same color can be selected from the bag is : a.18 b. 969 c. 649 d.108

A license plate is to consist of 2 letters followed by 4 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted.    A. 3,276,000   B. 3,275,980   C. 6,760,000   D. 3,276,140

The Venn diagram shows the number of people that answered a survey about where they go grocery shopping. People who go to the grocery store 25 People who go to a farmer's market 36 8 According to the Venn diagram, if 60 people were surveyed, how many people shop at both the grocery store and the farmer's market?

A shoe company wants to test an updated model of a running shoe on its wear after one month of running. Which of the following describes a matched pairs design? They recruit 50 people who run on a regular basis to participate in their study. They will have the runners wear the shoes when they run for two months. After two O The subjects are numbered 1-50, and these numbers are put into a random number generator. The first 25 random numbers, ignoring repeats, represent the subjects assigned to the new model group. The remaining 25 subjects will wear the original model. months, the wear on the shoes will be determined using the depth of the tread and flexibility of the toe box. The wear between the new model and the original model will then be compared. The subjects' names are written on equal-sized slips of paper and placed into a hat. A researcher then reaches in and pulls out 25 slips of paper. These subjects are assigned to the new model group. The remaining 25 subjects will be…

Of the 58 students in a mathematics​ class, 22 are taking​ French, 24 are taking​ German, and 7 are taking both French and German.   How many students in the mathematics class are taking neither French nor​ German?   nothing students

Bart has six books: a novel, a biography, a dictionary, a self help book, a statistics text book, and a comic book. Bart's bookshelf has room for only three of the books. In how many ways can Bart choose and order three books?