In a school,there are 21 students in the cric | vedclass

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Question

(A) Let $C$,$H$,and $F$ represent the sets of students in the cricket,hockey,and football teams,respectively.Given:$n(C) = 21$,$n(H) = 26$,$n(F) = 29$

Vedclass · Accepted Answer

$43$

Vedclass · Answer

(A) Let $C$,$H$,and $F$ represent the sets of students in the cricket,hockey,and football teams,respectively.Given:$n(C) = 21$,$n(H) = 26$,$n(F) = 29$$n(H \cap C) = 14$,$n(H \cap F) = 15$,$n(F \cap C) = 12$$n(H \cap C \cap F) = 8$We need to find the total number of students,which is $n(C \cup H \cup F)$.Using the Principle of Inclusion-Exclusion:$n(C \cup H \cup F) = n(C) + n(H) + n(F) - [n(H \cap C) + n(H \cap F) + n(F \cap C)] + n(H \cap C \cap F)$$n(C \cup H \cup F) = 21 + 26 + 29 - [14 + 15 + 12] + 8$$n(C \cup H \cup F) = 76 - 41 + 8$$n(C \cup H \cup F) = 35 + 8 = 43$Thus,the total number of students is $43$.

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