Let U be the set of 35 students participating in the sports of Football, Basketball or volleyball. 6 of these students participate in all the sports and 7 of them do not participate in any sport. Those who play Football are 16 in total while it is known that 8 play both Basketball and Volleyball. Calculate how many students i. Play exactly Basketball and Volleyball and not Football ii. Play either Basketball only or Volleyball only.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 36SE: The number of 5-element subsets from a set containing n elements is equal to the number of 6-element...
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Let U be the set of 35 students participating in the sports of Football, Basketball or volleyball. 6 of these students participate in all the sports and 7 of them do not participate in any sport. Those who play Football are 16 in total while it is known that 8 play both Basketball and Volleyball. Calculate how many students i. Play exactly Basketball and Volleyball and not Football ii. Play either Basketball only or Volleyball only.
Expert Solution
Step 1

Let F, B, V denotes the sports Football, Basketball and  Volleyball respectively.

Given that 

n(U)=35

nF B V=6

nF B  V' = 7n(U)-n(F B  V)=735-n(F B  V)=7n(F B  V)=28     ................(1)

nF=16 ....................(2)nBV=8

Let assume that

n(FB)=xn(FV)=y

Step 2

Represent the given data in a venn diagram.

Advanced Math homework question answer, step 2, image 1

 

 

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