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.
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.
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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Question
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 denotes the sports Football, Basketball and Volleyball respectively.
Given that
Let assume that
Step 2
Represent the given data in a venn diagram.
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