Question Number 198332 by necx122 last updated on 17/Oct/23
$${Of}\:{men}\:{that}\:{attended}\:{a}\:{party},\:\mathrm{30}\:{of} \\ $$$${them}\:{wore}\:{coats},\:\mathrm{20}\:{wore}\:{ties}\:{and}\:\mathrm{10} \\ $$$${wore}\:{hats}.\:{There}\:{were}\:\mathrm{4}\:{men}\:{who}\:{wore} \\ $$$${coats}\:{and}\:{tie},\:{or}\:{tie}\:{and}\:{hat}\:{or}\:{coat}\:{and} \\ $$$${hat}.\:\mathrm{14}\:{men}\:{wore}\:{tie}\:{only}\:{with}\:{no} \\ $$$${coat}\:{and}\:{hat}.\:{Find}\:{the}\:{number}\:{of}\:{men} \\ $$$${who}\:{wore}: \\ $$$$\left.{a}\right)\:{coat},\:{tie}\:{and}\:{hat} \\ $$$$\left.{b}\right)\:{hat}\:{only}\:{with}\:{no}\:{coat}\:{and}\:{hat}. \\ $$
Commented by necx122 last updated on 17/Oct/23
$${Please}\:{help},\:{I}'{ve}\:{tried}\:{but}\:{failed}. \\ $$
Answered by AST last updated on 18/Oct/23
$$\mathrm{20}=\mathrm{14}+\mathrm{4}−{a}+\mathrm{4}−{a}+{a}\Rightarrow{a}=\mathrm{2} \\ $$$$\mathrm{10}=\mathrm{4}−{a}+\mathrm{4}−{a}+{a}+{b}\Rightarrow\mathrm{10}=\mathrm{8}−{a}+{b}\Rightarrow{b}=\mathrm{4} \\ $$
Commented by necx122 last updated on 18/Oct/23
Please explain with a Venn diagram so I can understand it. please.
Thank you
Commented by AST last updated on 18/Oct/23
Commented by necx122 last updated on 18/Oct/23
Thank you so so much