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If there is a 30 students playing basketball football volleyball and 14 of theme play football and 2 others play 3 all sports and 15 of theme play volleyball only and 4 play football and volleyball only and 7 play volleyball and basketball only how many players play all 3 sports

Sagot :

Yankeriiiidn

To determine the number of players who play all three sports, we can apply the principle of the Inclusion-Exclusion formula.

Let's denote the number of players who play football as F, basketball as B, and volleyball as V. According to the problem:

F = 14 (Football players)

B = 7 (Basketball players)

V = 15 (Volleyball players)

We are also given that 2 players play all three sports, and 4 players play both football and volleyball only. Using the Inclusion-Exclusion principle:

N(F ∪ B ∪ V) = N(F) + N(B) + N(V) - N(F ∩ B) - N(F ∩ V) - N(B ∩ V) + N(F ∩ B ∩ V)

Substitute the given values:

N(F ∪ B ∪ V) = 14 + 7 + 15 - 4 - 2 - 7 + 2

N(F ∪ B ∪ V) = 25

Therefore, the total number of players who play all three sports is 2.