Question

A college awarded 48 medals in volleyball, 21 in basketball and 30 in cricket. If these medals went to a total of 72 men and only 4 men got medals in all the three sports, how many received medals in exactly two of the three sports?one of these is floor division

Answer 1

Step-by-step explanation:

a college awarded 40 mdals

Answer 2

$Number \: medals \: awarded \: in$

$volleyball \: n(V) = 48$

$Number \: medals \: awarded \: in$

$basketball \: n(B) = 30$

$Number \: medals \: awarded \: in$

$Cricket \: n(C) = 30$

$Number \: of \: men \: medals \: in \: three$

$sports \: n( V \cap B \cap C ) = 4$

$Total \: medals \: n( V \cup B \cup C) = 72$

$Let \: number \: of \: men \: received \: medals$

$in \: exactly \: two \: of \: the \: 3 \:sports = x+y+z$

$Let \: n( V\cap B) = x + 4$

$n( B\cap C) = y + 4$

$n( C\cap V) = z + 4$

/* We know that , */

$n( V \cup B \cup C) = n(V)+n(B)+n(C) - n( V\cap B)$

$- n( B\cap C) - n( C\cap V) + n( V \cap B \cap C )$

$\implies 72 = 48+21+30-(x+4)-(y+4)-(z+4)+4$

$\implies 72 = 99 - x - y - z - 4 - 4 - 4 + 4$

$\implies x+y+z = 99 - 72- 8$

$\implies x+y+z = 99 - 80$

$\implies x+y+z = 19$

Therefore.,

$\red{number \: of \: men \: received \: medals}$

$\red{ in \: exactly \: two \: of \: the \: 3 \:sports}$

$\red{ (x+y+z)}\green { = 19}$

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